10,550 results on '"EULER equations"'
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2. Numerical study on flow and combustion properties of oblique detonation engine in a wide speed range.
- Author
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Wang, Yang, Chen, Fang, Meng, Yu, Mikhalchenko, Elena Victorovna, and Skryleva, Evgeniya Igorevna
- Subjects
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MACH number , *DETONATION waves , *INTERNAL waves , *EULER equations , *PROPULSION systems , *HYPERSONIC aerodynamics - Abstract
Ensuring safe flight is a fundamental prerequisite for developing hypersonic propulsion systems. A comprehensive investigation of the steady boundary associated with oblique detonation wave in a wide speed range was conducted, with the aim of exploring the feasibility of oblique detonation engine across a diverse array of flight conditions. In this study, the wedge angle applicable in a wide-speed range was acquired via the analysis of oblique detonation wave polar curve. The configuration of the internal injection oblique detonation engine was subsequently designed and established, considering the effect of fuel-air inhomogeneity and complex wave system interactions within a confined combustor. The compressible Euler equations coupled with a 9-species and 19-step chemical reaction mechanism are employed to simulate the oblique detonation process. Ultimately, the safe flight envelope of an air-breathing vehicle equipped with the internal injection oblique detonation engine is mapped across a broad range of Mach numbers, demonstrating the engine's capability to operate within the Mach 8 to 12 range. Furthermore, the findings reveal that decreasing either the flight Mach number or altitude results in unsteady oblique detonation wave within the internal injection oblique detonation engine combustor, however, reducing the equivalence ratio can stabilize the oblique detonation wave once again. This study provides valuable guidance for the design and wide-speed-range operation of an internal injection oblique detonation engine. • An Internal Injection Oblique Detonation Engine is proposed for flight Mach numbers from 8 to 12. • The safe flight envelope of an air-breathing vehicle equipped with the IIODE is obtained. • The steady boundary associated with oblique detonation wave in a wide speed range is studied. • The flow and combustion properties within the IIODE are discussed. • The impacts of flight Mach number, altitude height and equivalence ratio on the stability of ODW are analyzed. [ABSTRACT FROM AUTHOR]
- Published
- 2025
- Full Text
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3. Structural stability of steady subsonic Euler flows in 2D finitely long nozzles with variable end pressures.
- Author
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Li, Jun and Wang, Yannan
- Subjects
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EULER-Lagrange system , *STREAM function , *SHEAR flow , *BOUNDARY value problems , *STRUCTURAL stability , *SUBSONIC flow , *EULER equations - Abstract
This paper is devoted to studying structural stability of steady subsonic Euler flows in 2D finitely long nozzles. The reference flow is subsonic shear flows with general size of vorticity. The problem is described by the steady compressible Euler system. With admissible physical conditions and prescribed pressures at the entrances and the exits of the nozzles respectively, we establish unique existence and structural stability of this kind of subsonic shear flows. Due to the hyperbolic-elliptic coupled form of the Euler system in subsonic regions, the problem is reformulated via Lagrange transformation and then decoupled into an elliptic mode and two hyperbolic modes. The elliptic mode is a mixed type boundary value problem of second order quasilinear elliptic equation for the stream function. The hyperbolic modes are transport types to control the total energy and the entropy. Mathematically, the iteration scheme is executed in a weight Hölder space with low regularity. • 2-D subsonic Euler flow with physical boundary conditions. • Weighted Hölder space with optimally low regularity. • Reformulating 2-D compressible Euler system via Lagrange transformation. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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4. A free boundary inviscid model of flow-structure interaction.
- Author
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Kukavica, Igor and Tuffaha, Amjad
- Subjects
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EXISTENCE theorems , *ELASTIC plates & shells , *FLUIDS , *A priori - Abstract
We obtain the local existence and uniqueness for a system describing interaction of an incompressible inviscid fluid, modeled by the Euler equations, and an elastic plate, represented by the fourth-order hyperbolic PDE. We provide a priori estimates for the existence with the optimal regularity H r , for r > 2.5 , on the fluid initial data and construct a unique solution of the system for initial data u 0 ∈ H r for r ≥ 3. An important feature of the existence theorem is that the Taylor-Rayleigh instability does not occur. This is in contrast to the free-boundary Euler problem, where the stability condition on the initial pressure needs to be imposed. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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5. FPGA Implementation for a Class of Generalized Hamiltonian Conservative Chaotic Systems Based on Integrated 4D Euler Equations with Multistability.
- Author
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Jia, Hongyan, Li, Wei, Wang, Hejin, Han, Xiaoguang, and Wang, Shiming
- Subjects
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EULER equations , *NUMERICAL analysis , *LYAPUNOV exponents , *HAMILTONIAN systems , *PHASE diagrams - Abstract
In this paper, two newly proposed generalized Hamiltonian Conservative Chaotic Systems (CCSs) based on integrated 4D Euler equations are first discussed. Second, another generalized Hamiltonian CCS is also proposed. Furthermore, a class of generalized Hamiltonian CCSs based on integrated 4D Euler equations is given and studied. Subsequently, numerical analysis for the class of generalized Hamiltonian CCSs is further investigated to show their advantages over most of the existing CCSs, where the corresponding Lyapunov exponents' diagrams, bifurcation diagrams and phase portraits are all given to show their multistability and complex dynamics. Finally, the class of generalized Hamiltonian CCSs is implemented by using FPGA technology, and the results observed in FPGA implementation are consistent with those observed in the numerical analysis. All these results not only show multistability from a physical point of view, but also provide new physical models for chaos applications. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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6. A WENO-Based Upwind Rotated Lattice Boltzmann Flux Solver with Lower Numerical Dissipation for Simulating Compressible Flows with Contact Discontinuities and Strong Shock Waves.
- Author
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Wang, Yunhao, Chen, Jiabao, Wang, Yan, Zeng, Yuhang, and Ke, Shitang
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MACH number ,COMPRESSIBLE flow ,EULER equations ,ASTROPHYSICAL jets ,FINITE differences - Abstract
This paper presents a WENO-based upwind rotated lattice Boltzmann flux solver (WENO-URLBFS) in the finite difference framework for simulating compressible flows with contact discontinuities and strong shock waves. In the method, the original rotating lattice Boltzmann flux solver is improved by applying the theoretical solution of the Euler equation in the tangential direction of the cell interface to reconstruct the tangential flux so that the numerical dissipation can be reduced. The fluxes at each interface are evaluated using a weighted summation of lattice Boltzmann solutions in two local perpendicular directions decomposed from the direction vector so that the stability performance can be improved. To achieve high-order accuracy, both fifth and seventh-order WENO reconstructions of the flow variables in the characteristic spaces are carried out. The order accuracy of the WENO-URLBFS is evaluated and compared with the traditional Lax–Friedrichs scheme, Roe scheme, and the LBFS by simulating the advection of the density disturbance problem. It is shown that the fifth and seventh-order accuracy can be achieved by all considered flux-evaluation schemes, and the present WENO-URLBFS has the lowest numerical dissipation. The performance of the WENO-URLBFS is further examined by simulating several 1D and 2D examples, including shock tube problems, Shu–Osher problems, blast wave problems, double Mach reflections, 2D Riemann problems, K-H instability problems, and High Mach number astrophysical jets. Good agreements with published data have been achieved quantitatively. Moreover, complex flow structures, including shock waves and contact discontinuities, are successfully captured. The present WENO-URLBFS scheme seems to present an effective numerical tool with high-order accuracy, lower numerical dissipation, and strong robustness for simulating challenging compressible flow problems. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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7. A dissipative extension to ideal hydrodynamics.
- Author
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Hatton, Marcus John and Hawke, Ian
- Subjects
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EULER equations , *BULK viscosity , *EQUATIONS of motion , *STELLAR mergers , *NEUTRON stars - Abstract
We present a formulation of special relativistic dissipative hydrodynamics (SRDHD) derived from the well-established Müller–Israel–Stewart (MIS) formalism using an expansion in deviations from ideal behaviour. By re-summing the non-ideal terms, our approach extends the Euler equations of motion for an ideal fluid through a series of additional source terms that capture the effects of bulk viscosity, shear viscosity, and heat flux. For efficiency these additional terms are built from purely spatial derivatives of the primitive fluid variables. The series expansion is parametrized by the dissipation strength and time-scale coefficients, and is therefore rapidly convergent near the ideal limit. We show, using numerical simulations, that our model reproduces the dissipative fluid behaviour of other formulations. As our formulation is designed to avoid the numerical stiffness issues that arise in the traditional MIS formalism for fast relaxation time-scales, it is roughly an order of magnitude faster than standard methods near the ideal limit. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
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8. Global well-posedness and large-time behavior of classical solutions to the Euler-Navier-Stokes system in [formula omitted].
- Author
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Huang, Feimin, Tang, Houzhi, Wu, Guochun, and Zou, Weiyuan
- Subjects
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NAVIER-Stokes equations , *DRAG force , *TWO-phase flow , *CAUCHY problem , *EULER equations , *EQUILIBRIUM - Abstract
In this paper, we study the Cauchy problem of a two-phase flow system consisting of the compressible isothermal Euler equations and the incompressible Navier-Stokes equations coupled through the drag force, which can be formally derived from the Vlasov-Fokker-Planck/incompressible Navier-Stokes equations. When the initial data is a small perturbation around an equilibrium state, we prove the global well-posedness of the classical solutions to this system and show the solutions tends to the equilibrium state as time goes to infinity. In order to resolve the main difficulty arising from the pressure term of the incompressible Navier-Stokes equations, we properly use the Hodge decomposition, spectral analysis, and energy method to obtain the L 2 time decay rates of the solution when the initial perturbation belongs to L 1 space. Furthermore, we show that the above time decay rates are optimal. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
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9. The stabilizing effect of temperature and magnetic field on a 2D magnetic Bénard fluids.
- Author
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Lai, Suhua, Shen, Linxuan, Ye, Xia, and Zhao, Xiaokui
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MAGNETIC field effects , *MAGNETIC fluids , *MAGNETIC fields , *EULER equations , *HYDRAULIC couplings - Abstract
In this paper we study the stability of a special magnetic Bénard system near equilibrium, where there exists Laplacian magnetic diffusion and temperature damping but the velocity equation involves no dissipation. Without any velocity dissipation, the fluid velocity is governed by the two-dimensional incompressible Euler equation, whose solution can grow rapidly in time. However, when the fluid is coupled with the magnetic field and temperature through the magnetic Bénard system, we show that the solution is stable. Our results mathematically illustrate that the magnetic field and temperature have the effect of enhancing dissipation and contribute to stabilize the fluid. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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10. Non-uniform dependence on initial data for the Euler equations in Besov spaces.
- Author
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Li, Jinlu, Yu, Yanghai, and Zhu, Weipeng
- Subjects
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BESOV spaces , *INITIAL value problems , *EULER equations - Abstract
In this paper, we consider the initial value problem to the higher dimensional Euler equations in the whole space. Based on the local well-posedness result and the lifespan, we prove that the data-to-solution map of this problem is not uniformly continuous in nonhomogeneous Besov spaces. Our obtained result improves considerably the previous results given by Himonas-Misiołek (2010) [8] and Pastrana (2021) [21]. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
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11. A simple model of a gravitational lens from geometric optics.
- Author
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Szafraniec, Bogdan and Harford, James F.
- Subjects
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INTEGRAL calculus , *REFRACTIVE index , *EULER equations , *HYPERBOLIC functions , *TRIGONOMETRIC functions , *GRAVITATIONAL lenses - Abstract
We propose a simple geometric optics analog of a gravitational lens with a refractive index equal to one at large distances and scaling like n (r) 2 = 1 + C 2 / r 2 , where C is a constant. We obtain the equation for ray trajectories from Fermat's principle of least time and the Euler equation. Our model yields a very simple ray trajectory equation. The optical rays bending, reflecting, and looping around the lens are all described by a single trigonometric function in polar coordinates. Optical rays experiencing fatal attraction are described by a hyperbolic function. We use our model to illustrate the formation of Einstein rings and multiple images. Editor's Note: This article describes a simple theoretical model for gravitational lensing. The authors analyze a graded index of refraction that reproduces the behavior for light passing near the event horizon of a black hole. The mathematical simplicity of the model permits exploration of the effects of gravitational lensing—including bending, reflection, and the formation of Einstein rings—using only integral calculus and Fermat's principle. The authors illustrate many interesting lensing phenomena with 2D and 3D graphics. The model described in this paper could be introduced as a "theoretical toy model" to complement classroom demonstrations of gravitational lensing such as a "logarithmic lens" or the stem of a wine glass, making gravitational lensing and its use in modern astrophysics accessible to introductory physics students. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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12. On metallic-type asteroid rotation moving in magnetic field (introducing magnetic second-grade YORP effect).
- Author
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Ershkov, S.V. and Shamin, R.V.
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ANGULAR momentum (Mechanics) , *OUTER space , *EULER equations , *ORTHOGONAL surfaces , *METALLIC surfaces , *ASTEROIDS - Abstract
A novel physical effect has been found to be illuminated of being physically self-consistent to take into account in further calculating the dynamics of magnetically-induced asteroid rotation, surface of which has mostly a conducting structure (whereas such mostly metallic-formed asteroid is assumed to be moving in an external magnetic field of planet but in the meantime to be orbiting preferably outside its sphere of effective attraction). The last condition of asteroid surface's having conducting structure means the existence of the applied external torques stemming from the physical interactions between external magnetic field and iron asteroid itself (including long-term effect due to torques stemming from arising eddy-currents on metallic surface of asteroid). Such eddy-currents should heat the conducting surface of asteroid with further non-uniformly re-directing the heat flow from surface of asteroid into outer space via fluxes of thermal photons which carry momentum (in orthogonal direction to the surface which is in most cases far from the ideal surface of sphere). This leads by taking into account the overall outcome of heat flow (from the non-ideal surface of asteroid) to a kind of long-term magnetic second-grade YORP effect. System of Euler equations for aforementioned dynamics of asteroid magnetic rotation has been investigated in regard to existence of semi-analytical solution. Various perturbations (such as collisions, YORP effect) may destabilize the rotation of asteroid deviating it from the current spin state, whereas the electric(eddy)current-induced dissipation of energy reduces kinetic one of asteroid spin. So, dynamics of the asteroid rotation should result in a spinning about maximal-inertia axis with the proper spin state corresponding to minimal energy with a fixed angular momentum. • New physical effect is found for magnetically-induced metallic asteroid rotation. • Metallic-formed asteroid is assumed to be moving in an external magnetic field. • Conducting structure means torques stemming from an eddy-currents on its surface. • Overall outcome of non-iniform heat flow forms magnetic second-grade YORP effect. • Evolution of spin towards rotation about maximal-inertia axis is approximated. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
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13. Euler-α equations in a three-dimensional bounded domain with Dirichlet boundary conditions
- Author
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Yuan Shaoliang, Huang Lehui, Cheng Lin, and You Xiaoguang
- Subjects
non-newtonian fluids ,well-posedness for pdes ,euler-α equations ,euler equations ,35a01 ,35d35 ,35q35 ,Mathematics ,QA1-939 - Abstract
In this article, we investigate the Euler-α\alpha equations in a three-dimensional bounded domain. On the one hand, we prove in the Euler setting that the equations are locally well-posed with initial data in Hs(s≥3){H}^{s}\left(s\ge 3). On the other hand, the relationship between the Hs{H}^{s}-norm of the velocity field and the parameter α\alpha is clarified.
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- 2024
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14. Stability and related zero viscosity limit of steady plane Poiseuille-Couette flows with no-slip boundary condition.
- Author
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Jiang, Song and Zhou, Chunhui
- Subjects
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COUETTE flow , *NAVIER-Stokes equations , *BOUNDARY layer (Aerodynamics) , *SHEAR flow , *VISCOSITY solutions , *EULER equations - Abstract
We study the existence and stability of smooth solutions to the steady Navier-Stokes equations near plane Poiseuille-Couette flow in the absence of any external force in two-dimensional domain Ω = (0 , L) × (0 , 2). Under the assumption 0 < L ≪ 1 , we prove that there exist smooth solutions to the steady Navier-Stokes equations which are stable under infinitesimal perturbations of plane Poiseuille-Couette flow. In particular, if the basic flow is the Couette flow, then through a formal asymptotic expansion including the Euler correctors and weak boundary layer correctors with different scales near the rigid walls y = 0 and y = 2 , we can prove that for any finite disturbance o (1) of the Couette flow in horizontal direction, there still exist stable smooth solutions to the steady Navier-Stokes equations. Finally, based on the same linear estimates, we establish the zero viscosity limit of the solutions obtained above to the solutions of the steady Euler equations. [ABSTRACT FROM AUTHOR]
- Published
- 2025
- Full Text
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15. High-order gas-kinetic scheme with TENO class reconstruction for the Euler and Navier-Stokes equations.
- Author
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Mu, Junlei, Zhuo, Congshan, Zhang, Qingdian, Liu, Sha, and Zhong, Chengwen
- Subjects
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NAVIER-Stokes equations , *EULER equations , *ADAPTIVE control systems , *STENCIL work , *EQUILIBRIUM - Abstract
The high-order gas-kinetic scheme (HGKS) with WENO spatial reconstruction method has been extensively validated through numerous numerical experiments, demonstrating its superior accuracy, efficiency and robustness. In comparison to WENO class schemes, TENO class schemes exhibit significantly improved robustness, low numerical dissipation and sharp discontinuity capturing. This paper introduces two types of fifth-order HGKS utilizing TENO class schemes. One approach involves replacing the WENO scheme with the TENO scheme in the conventional WENO GKS. Both WENO and TENO schemes provide non-equilibrium state values at the cell interface. The slopes of the non-equilibrium state, as well as the values and slopes of the equilibrium state, are obtained through additional linear reconstruction. Another type of HGKS scheme named TENO GKS with adaptive order (TENO-A GKS), is similar to most multi-resolution HGKS schemes. Following a robust scale-separation procedure, a tailored ENO-like stencil selection strategy is proposed to ensure that high-order accuracy is maintained in smooth regions by selecting the candidate reconstruction from a large stencil, while enforcing the ENO property near discontinuities by adopting the candidate reconstruction from small smooth stencils. These TENO schemes include TENO schemes with adaptive accuracy order and adaptive dissipation control (TENO-AA) and TENO schemes with dual ENO-like stencil selection (TENO-D). The HGKS scheme based on TENO-A reconstruction takes advantage of the large stencil to provide point values and slopes of the non-equilibrium states. By dynamically merging the reconstructed non-equilibrium slopes, the need for extra reconstruction of the equilibrium states at the beginning of each time step can be avoided. The simple TENO-A GKS scheme exhibits better robustness compared to the conventional WENO GKS or TENO GKS. [ABSTRACT FROM AUTHOR]
- Published
- 2025
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16. General Solutions to the Navier-Stokes Equations for Incompressible Flow
- Author
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JangRyong Shin
- Subjects
navier-stokes equations ,euler equations ,helmholtz equation ,bernoulli’s principle ,beltrami flow ,water wave ,Ocean engineering ,TC1501-1800 - Abstract
Waves are mainly generated by wind via the transfer of wind energy to the water through friction. When the wind subsides, the waves transition into swells and eventually dissipate. Friction plays a crucial role in the generation and dissipation of waves. Numerous wave theories have been developed based on the assumption of inviscid flow, but these theories are inadequate in explaining the transformation of waves into swells. This study addressed these limitations by analytically deriving general solutions to the Navier–Stokes equations. By expressing the velocity field as the product of a solution to the Helmholtz equation and a time-dependent univariate function, the Navier–Stokes equations are decomposed into an ordinary differential equation and the Euler equations, which are solved using tensor calculus. This paper provides solutions for viscous flow with shear currents when applied to the water wave problem. These solutions were validated through their application to the vorticity equation. The decay modulus of water waves was compared with experimental data, showing a significant degree of concordance. In contrast to other wave theories, this study clarified the process through which waves evolve into swells.
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- 2024
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17. Recent developments in mathematical aspects of relativistic fluids.
- Author
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Disconzi, Marcelo
- Subjects
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FLUID dynamics , *RESEARCH personnel , *GRADUATE students , *FLUIDS , *VISCOSITY , *EULER equations - Abstract
We review some recent developments in mathematical aspects of relativistic fluids. The goal is to provide a quick entry point to some research topics of current interest that is accessible to graduate students and researchers from adjacent fields, as well as to researches working on broader aspects of relativistic fluid dynamics interested in its mathematical formalism. Instead of complete proofs, which can be found in the published literature, here we focus on the proofs' main ideas and key concepts. After an introduction to the relativistic Euler equations, we cover the following topics: a new wave-transport formulation of the relativistic Euler equations tailored to applications; the problem of shock formation for relativistic Euler; rough (i.e., low-regularity) solutions to the relativistic Euler equations; the relativistic Euler equations with a physical vacuum boundary; relativistic fluids with viscosity. We finish with a discussion of open problems and future directions of research. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
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18. Numerical Study of Shock Wave Interaction with V-Shaped Heavy/Light Interface.
- Author
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Alsaeed, Salman Saud and Singh, Satyvir
- Subjects
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MACH number , *SHOCK waves , *VORTEX motion , *KINETIC energy , *COMPUTER simulation , *EULER equations - Abstract
This paper investigates numerically the shock wave interaction with a V-shaped heavy/light interface. For numerical simulations, we choose six distinct vertex angles ( θ = 40 ∘ , 60 ∘ , 90 ∘ , 120 ∘ , 150 ∘ , and 170 ∘) , five distinct shock wave strengths ( M s = 1.12 , 1.22 , 1.30 , 1.60 , and 2.0 ), and three different Atwood numbers ( A t = − 0.32 , − 0.77 , and − 0.87 ). A two-dimensional space of compressible two-component Euler equations are solved using a third-order modal discontinuous Galerkin approach for the simulations. The present findings demonstrate that the vertex angle has a crucial influence on the shock wave interaction with the V-shaped heavy/light interface. The vertex angle significantly affects the flow field, interface deformation, wave patterns, spike generation, and vorticity production. As the vertex angle decreases, the vorticity production becomes more dominant. A thorough analysis of the vertex angle effect identifies the factors that propel the creation of vorticity during the interaction phase. Notably, smaller vertex angles lead to stronger vorticity generation due to a steeper density gradient, while larger angles result in weaker, more dispersed vorticity and a less complex interaction. Moreover, kinetic energy and enstrophy both dramatically rise with decreasing vortex angles. A detailed analysis is also carried out to analyze the vertex angle effects on the temporal variations of interface features. Finally, the impacts of different Mach and Atwood numbers on the V-shaped interface are briefly presented. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
19. Dynamic of an inhomogeneous three-layer sphere under cyclic pressure.
- Author
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Zhang, Xi-meng and Qi, Hui
- Subjects
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SPHERICAL waves , *ALGEBRAIC equations , *STRESS concentration , *EULER equations , *FINITE element method - Abstract
In this paper, the dynamic characteristics of inhomogeneous three-layer spheres under spherical wave induced by cyclic pressure are studied. The density is assumed to have a square of inverse proportional function distribution along the radius. Firstly, on the basis of Lamb decomposition and variable separation method, the analytical expression of spherical wave is conducted, which satisfies the stress equilibrium on the outer and inner surfaces of the sphere, and the Euler equation is obtained due to inhomogeneity. Next, algebraic equations with respective boundary conditions are composed and solved by effective truncation techniques. Finally, a comparison and discussion are conducted between the model presented in this article and the homogeneous model obtained by the Legendre polynomial expansion. Obtained results enable to reveal the influence on the dynamic stress concentration factor intensity under proper conditions. The conclusions of this article are verified by comparing the analytical solutions to the ones obtained by finite element method. This paper can provide a theoretical method for the analysis of mechanical properties of inhomogeneous multilayered spherical structure under dynamic loading. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
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20. Impact of a two-dimensional steep hill on wind turbine noise propagation.
- Author
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Colas, Jules, Emmanuelli, Ariane, Dragna, Didier, Blanc-Benon, Philippe, Cotté, Benjamin, and Stevens, Richard J. A. M.
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SOUND pressure ,WIND turbines ,EULER equations ,ACOUSTIC wave propagation ,AMPLITUDE modulation - Abstract
Wind turbine noise propagation in a hilly terrain is studied through numerical simulation in different scenarios. Linearized Euler equations are solved in a moving frame that follows the wavefront, and wind turbine noise is modeled with an extended moving source. We employ large-eddy simulations to simulate the flow around the hill and the wind turbine. The sound pressure levels (SPLs) obtained for a wind turbine in front of a 2D hill and a wind turbine on a hilltop are compared to a baseline flat case. First, the source height and wind speed strongly affect sound propagation downwind. We find that topography influences the wake shape, inducing changes in the sound propagation that drastically modify the SPL downwind. Placing the turbine on the hilltop increases the average sound pressure level and amplitude modulation downwind. For the wind turbine placed upstream of a hill, a strong shielding effect is observed. But, because of the refraction by the wind gradient, levels are comparable with the baseline flat case just after the hill. Thus, considering how terrain topography alters the flow and wind turbine wake is essential to accurately predict wind turbine noise propagation. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
21. Axisymmetric Forced Vibration of Hydro-Elastic System Consisting of Pre-Strained Highly Elastic Plate, Compressible Inviscid Fluid and Rigid Wall*.
- Author
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Akbarov, S. D., Imamaliyeva, J. N., and Zamanov, A. D.
- Subjects
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LIQUID-liquid interfaces , *EULER equations , *ELASTIC plates & shells , *FLUID flow , *INTEGRAL transforms - Abstract
The present paper studies the axisymmetric forced vibrations of the hydro-elastic system consisting of the plate made of a highly elastic material with axisymmetric finite initial strains, barotropic inviscid compressible fluid, and rigid wall restricting the fluid flow. The motion of the plate is described using the equations and relations of the three-dimensional linearized theory of elastic waves in bodies with initial stresses. However, the flow of the fluid is described by the linearized Euler equations for the inviscid compressible fluids. Guz's presentations for the general solution of the mentioned linearized equations are used to solve these equations for the corresponding boundary and compatibility conditions. The corresponding equations concerning these transforms are solved analytically using the Hankel integral transform. The originals of the sought values are found numerically by employing the authors' calculation algorithm and PC programs. Numerical results on the frequency response of the interface pressure are presented and discussed. In particular, it is established that the initial radial stretching of the plate leads to the decrease in the interface pressure. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
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22. Effect of Half-Space of Ideal Fluid on Surface Instability of Incompressible Elastic Layer Subjected to Finite Initial Deformations.
- Author
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Bagno, A. M. and Shchuruk, G. I.
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LAMB waves , *PHASE velocity , *ELASTIC waves , *ELASTIC deformation , *THEORY of wave motion , *EULER equations - Abstract
A problem of the propagation of normal waves in an incompressible elastic layer interacting with the half-space of ideal compressible fluid is stated and solved. The dispersion curves of normal generalized waves in a hydroelastic system over a wide range of frequencies are constructed using the three-dimensional linearized equations of the elasticity theory of finite deformations for a solid and the three-dimensional linearized Euler equations for ideal compressible fluid. The effect of finite initial deformations in the incompressible elastic layer as well as the half-space of ideal compressible fluid on the phase velocities, dispersion of generalized modes, and surface instability of the hydroelastic waveguide is analyzed. The numerical results presented in the form of plots are considered. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
23. Gauge-invariant quantum fields.
- Author
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Quadri, A.
- Subjects
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GREEN'S functions , *NONABELIAN groups , *DIFFERENTIAL equations , *EULER equations , *ABELIAN functions - Abstract
Gauge-invariant quantum fields are constructed in an Abelian power-counting renormalizable gauge theory with both scalar, vector and fermionic matter content. This extends previous results already obtained for the gauge-invariant description of the Higgs mode via a propagating gauge-invariant field. The renormalization of the model is studied in the Algebraic Renormalization approach. The decomposition of Slavnov–Taylor identities into separately invariant sectors is analyzed. We also comment on some non-renormalizable extensions of the model whose 1-PI Green's functions are the flows of certain differential equations of the homogeneous Euler type, exactly resumming the dependence on a certain set of dim. 6 and dim. 8 derivative operators. The latter are identified uniquely by the condition that they span the mass and kinetic terms in the gauge-invariant dynamical fields. The construction can be extended to non-Abelian gauge groups. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
24. Non-limited vibrational effect on shock-induced phase transitions of condensed fluid in hard-sphere model.
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Zheng, Yue, Xu, Junjun, and Tang, Ke
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PHASE transitions , *EULER equations , *SHOCK waves , *CONDENSED matter , *LIBERTY - Abstract
The essence of fluid phase transition is the jump of physical properties distinctly induced by shock waves in the hard-sphere model. Due to the strong impact of the wave, the internal freedoms of molecules are stimulated, releasing tremendous energy that commonly triggers the phase transition. Conversely, typical thermal and dynamic jumps can be described by the Rankine–Hugoniot conditions based on the Euler equation. In the theoretical simulation, the initial density and rotational freedoms of molecules are directly regarded as the primary factors to affect processes of phase transition. However, the influence of vibrational freedom in molecules has not been discussed yet. As the increasing temperature can gradually excite the affection of vibrational freedom, it is unwise to assume that the temperature element is constant in the theory. What would be a suitable model that accurately reflects the relationship between temperature and affection from vibrational freedom? The non-limited model has been courageously attempted with the temperature range from T0 to 6T0 (T0 is unperturbed temperature). We have found that the vibrational freedom can have a great effect on properties during phase transition processes. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
25. برآورد تأثیر توهم پولی بر تابع مطلوبیت خانوارهای ایرانی رهیافت معادلات اولر.
- Author
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رضا روشن
- Abstract
Purpose: Extensive evidence shows that consumption-based asset pricing models (CCAPM) proposed by Lucas (1978) and Breeden (1979) have failed to explain average stock returns in cross-sectional data. In this context, we can refer to the studies of Breeden, Gibbons and Litzenberg (1989), Letas and Ludwigson (2001), and Jacobs and Wong (2004). In response to this failure, several studies used other variables than consumption growth in a single-factor model to improve the performance of the mentioned structure (such as Parker and Julliard (2005), Jaganthan and Wong (2007), Savo (2011) and Kroenke (2017)). In none of the domestic studies, inflation has been used as a risk factor. Therefore, this study aims to fill this gap by focusing on the impact of monetary illusion on the desirability of Iranian households in the period under review. In fact, this research is of novelty compared to the previous studies conducted inside the country. Firstly, with the inclusion of the inflation variable in the household preferences function, the CCAPM model has been developed in such a way that the inflation variable can be included in the household preferences function. Secondly, reversible preferences and non-reversible power utility have been used to estimate the monetary illusion parameter. Thirdly, in this research, the system of equations includes the return of various assets such as bank interest rate, stock return, housing return and labor wage return, and the parameters of the equations have been estimated by using different appropriate tools. Methodology: In order to include inflation as a risk factor and define a parameter that shows the degree of monetary illusion of brokers, Mayo (2018) specified a threefactor macro model for asset pricing including inflation rate, consumption growth and asset yield in the CCAPM structure. The underlying framework of the model includes a recursive inter-period utility presented by Epstein-Zine and Weil (1989). This framework made use of an intra-period utility function that corresponds to both real consumption growth and nominal consumption growth (with the specification a CobbDouglas function). Intra-period utility is appropriate for a case where the investor faces a partial monetary illusion, which is because he cannot fully distinguish real consumption from nominal consumption in his consumption/asset allocation decision. The degree of monetary illusion is represented by the monetary illusion parameter (ϵ), which varies from zero to one. Therefore, the assumption of monetary illusion allows the researcher to create a model in which the inflation variable is used as an endogenous risk factor in the pricing kernel. In this regard, there are three preferences parameters in the created model, including relative risk aversion coefficient, monetary illusion parameter, and inter-period substitution elasticity. In this study, inflation is included in the function of households' preferences in the form of consumption capital asset pricing model (CCAPM) so as to estimate the impact of money illusion on the utility of Iranian households in the period of 1978- 2021 To this end, the recursive preferences function provided by Epstein-Zin and a non-recursive power utility function with constant relative risk aversion are used in such a way that the inflation growth variable appears as a risk factor in the stochastic discount factor of the derived Euler equations. In fact, inflation arises endogenously in the pricing kernel by assuming an intra-temporal utility that depends on both real and nominal consumption. This suits an investor with partial money illusion. Then, the generalized moments method (GMM), MAE and MSE criteria are used to estimate the systems of equations and select the most appropriate model. Findings and discussion: After the mentioned models are estimated, the mean absolute magnitude of errors (MAE) and mean squared errors (MSE) criteria are used to select the best model among the fitted ones. The results show that the model with recursive preferences has the lowest values for the two mentioned statistics. Therefore, this model is chosen as the best one, based on which the effect of monetary illusion on the utility function of Iranian households has been 18% during the period under review. The criteria prove the superiority of recursive preferences. The results of the research also indicate that the money illusion parameter is statistically significant, and Hansen's J statistics confirm the appropriateness of the instruments. In the superior model, the effect of money illusion on the desirability of households is 0.18. The significance of the coefficients and the fit statistics of the models show that the inclusion of the data related to inflation growth in capital asset pricing models as a risk factor alongside the risk factor of consumption growth and asset return portfolio is significant. Conclusions and policy implications: The findings show that, in the first model where return preferences are used, the effect of monetary illusion on consumers' desirability is 0.18. Also, in the second model, which is bounded by the first model and involves non-reversibility and ability utility, the effect of monetary illusion on the utility of Iranian households is 0.03. In both estimates, all the coefficients are statistically significant, and the diagnostic tests for the remaining phrases confirm the correctness of the estimates. After the models are estimated, the mean absolute magnitude of errors (MAE) and the mean squared errors (MSE) criteria are used to select the best model among the fitted ones. The results show that the model with recursive preferences has the lowest values in the two types of statistics. Therefore, this model is chosen as the best one. Based on it, the effect of monetary illusion on the utility function of Iranian households is found to have been 18% during the period under review. Considering the relative impact of monetary illusion on the utility of households, it is necessary for policy makers and planners to reduce and control prices in order to better adapt the utility of households to economic realities. [ABSTRACT FROM AUTHOR]
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- 2024
26. A revisit to the pressureless Euler–Navier–Stokes system in the whole space and its optimal temporal decay.
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Choi, Young-Pil, Jung, Jinwook, and Kim, Junha
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DRAG force , *HEAT equation , *EULER-Lagrange equations , *NAVIER-Stokes equations , *MULTIPHASE flow , *EULER equations - Abstract
In this paper, we present a refined framework for the global-in-time well-posedness theory for the pressureless Euler–Navier–Stokes system and the optimal temporal decay rates of certain norms of solutions. Here the coupling of two systems, pressureless Euler system and incompressible Navier–Stoke system, is through the drag force. We construct the global-in-time existence and uniqueness of regular solutions for the pressureless Euler–Navier–Stokes system without using a priori large time behavior estimates. Moreover, we seek for the optimal Sobolev regularity for the solutions. Concerning the temporal decay for solutions, we show that the fluid velocities exhibit the same decay rate as that of the heat equations. In particular, our result provides that the temporal decay rate of difference between two velocities, which is faster than the fluid velocities themselves, is at least the same as the second-order derivatives of fluid velocities. [ABSTRACT FROM AUTHOR]
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- 2024
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27. Solitary solutions to the steady Euler equations with piecewise constant vorticity in a channel.
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Matthies, Karsten, Sewell, Jonathan, and Wheeler, Miles H.
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VORTEX motion , *STAGNATION point , *EULER equations , *INVISCID flow , *SHEAR flow , *ASYMPTOTIC expansions , *EULER-Lagrange equations - Abstract
We consider a two-dimensional, two-layer, incompressible, steady flow, with vorticity which is constant in each layer, in an infinite channel with rigid walls. The velocity is continuous across the interface, there is no surface tension or difference in density between the two layers, and the flow is inviscid. Unlike in previous studies, we consider solutions which are localised perturbations rather than periodic or quasi-periodic perturbations of a background shear flow. We rigorously construct a curve of exact solutions and give the leading order terms in an asymptotic expansion. We also give a thorough qualitative description of the fluid particle paths, which can include stagnation points, critical layers, and streamlines which meet the boundary. [ABSTRACT FROM AUTHOR]
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- 2024
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28. Machine learning-based WENO5 scheme.
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Nogueira, Xesús, Fernández-Fidalgo, Javier, Ramos, Lucía, Couceiro, Iván, and Ramírez, Luis
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SCIENTIFIC knowledge , *COMPUTATIONAL fluid dynamics , *PATTERNMAKING , *FINITE differences , *EULER equations - Abstract
Machine learning (ML) is becoming a powerful tool in Computational Fluid Dynamics (CFD) to enhance the accuracy, efficiency, and automation of simulations. Currently, in the design of shock-capturing methods, there is still a heavy reliance on the expertise and scientific knowledge of each author, particularly in nonlinear components such as smoothness indicators and weighting functions. ML has the potential to reduce this dependency, since by leveraging large datasets, they can learn intricate patterns and make accurate predictions of these functions. In this work we present a neural network that compute the weighting functions in the WENO5 scheme. The proposed WENO5-NN scheme generalizes well for different resolutions, and in most of the cases tested, it outperforms the classical WENO5-JS scheme. • Neural network to compute the weighting functions for WENO5 schemes. • The proposed scheme generalizes for different grid resolutions and problems. • The neural-network based scheme outperforms several WENO5 schemes. [ABSTRACT FROM AUTHOR]
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- 2024
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29. Riemann Problem for the Isentropic Euler Equations of Mixed Type in the Dark Energy Fluid.
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Chen, Tingting, Jiang, Weifeng, Li, Tong, Wang, Zhen, and Lin, Junhao
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RIEMANN-Hilbert problems , *EULER equations , *SHOCK waves , *DARK energy , *ELLIPTIC curves - Abstract
We are concerned with the Riemann problem for the isentropic Euler equations of mixed type in the dark energy fluid. This system is non-strictly hyperbolic on the boundary curve of elliptic and hyperbolic regions. We obtain the unique admissible shock waves by utilizing the viscosity criterion. Assuming fixed left states are in the elliptic and hyperbolic regions, respectively, we construct the unique Riemann solution for the mixed-type models with the initial right state in some feasible regions. Finally, we present numerical simulations which are consistent with our theoretical results. [ABSTRACT FROM AUTHOR]
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- 2024
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30. (2+1)-Dimensional Fifth-Order KdV Equation and (2+1)-Dimensional Gardner Equation Obtained from Ideal Fluid Model Revisited—Solitary Wave Solutions.
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Karczewska, Anna and Rozmej, Piotr
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EULER equations ,EQUATIONS ,FLUIDS - Abstract
The (2+1)-dimensional fifth-order KdV equation and (2+1)-dimensional Gardner equation obtained by us using Euler equations for an ideal fluid model in 2023 are revisited. Including additional second-order corrections enabled the derivation of the (2+1)-dimensional fifth-order KdV and Gardner equations without relying on the additional assumptions previously required. The new forms of these equations include an additional non-local term, which allows for the existence of families of solitary wave solutions analogous to solutions to those of the (1+1)-dimensional fifth-order KdV and Gardner equations. [ABSTRACT FROM AUTHOR]
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- 2024
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31. On uniqueness of steady 1-D shock solutions in a finite nozzle via asymptotic analysis for physical parameters.
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Fang, Beixiang, Jiang, Su, and Sun, Piye
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THERMAL conductivity , *INVISCID flow , *SHOCK waves , *VISCOSITY , *EULER equations , *NOZZLES , *NAVIER-Stokes equations - Abstract
In this paper, we study the uniqueness of the steady 1-D shock solutions for the inviscid compressible Euler system in a finite nozzle via asymptotic analysis for physical parameters. The parameters for the heat conductivity and the temperature-depending viscosity are investigated for both barotropic gases and polytropic gases. It finally turns out that the hypotheses on the physical effects have significant influences on the asymptotic behaviors as the parameters vanish. In particular, the positions of the shock front for the limit shock solution (if exists) are different for different hypotheses. Hence, it seems impossible to figure out a criterion selecting the unique shock solution within the framework of the inviscid Euler flows. [ABSTRACT FROM AUTHOR]
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- 2024
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32. Euler Characteristic Computation by Means of a Chain Code Applied to Binary Images.
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Gómez-Gómez, Elisa I. and Sánchez-Cruz, Hermilo
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EULER characteristic , *IMAGE compression , *EULER equations , *BINARY codes , *GEOMETRY - Abstract
This paper presents a new approach for calculating the Euler characteristic in 2D binary images. The problem is addressed using the Three OrThogonal symbol chain code (3OT code), using only one symbol for the calculation of the Euler characteristic. Using this code, it is possible to introduce new geometric concepts represented by the same symbol of the 3OT alphabet and to simplify the overall equation of the Euler characteristic. This process is supported by the proof of a set of theorems and their numerical validation, using a set of binary images with a variable number of holes. Thus, this research proves that the 3OT code can be used not only for image compression as reported in the literature, but also to simplify the expression of the Euler characteristic as well as for the analysis and simplification of the shape of contours. [ABSTRACT FROM AUTHOR]
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- 2024
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33. Exploration of solitons and analytical solutions by sub-ODE and variational integrators to Klein-Gordon model.
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Rizvi, Syed T. R., Ghafoor, Sana, Seadawy, Aly R., Arnous, Ahmed H., AL Garalleh, Hakim, and Shah, Nehad Ali
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OPTICAL fiber detectors ,LAGRANGE equations ,PLASMA physics ,BOSE-Einstein condensation ,EULER equations ,SINE-Gordon equation - Abstract
In this paper, we use the sub-ODE method to analyze soliton solutions for the renowned nonlinear Klein-Gordon model (NLKGM). This method provides a variety of soliton solutions, including three positive solitons, three Jacobian elliptic function solutions, bright solitons, dark solitons, periodic solitons, rational solitons and hyperbolic function solutions. Applications for these solitons can be found in optical communication, fiber optic sensors, plasma physics, Bose-Einstein condensation and other areas. We also study some numerical solutions by using forward, backward, and central difference techniques. Moreover, we discuss variational integrators (VIs) using the projection technique for NLKGM. We develop a numerical solution for NLKGM using the discrete Euler lagrange equation, the Lagrangian and the Euler lagrange equation. At the end, in various dimensions, covering 3D, 2D, and contour, we will also plot several graphs for the obtained NLKGM solutions. A contour plot is a type of graphic representation that displays a three-dimensional surface on a two-dimensional plane by using contour lines. Each contour line in the plotted function represents one of the function's constant values, mapping the function's value across the plane. This model has been studied across multiple soliton solutions using various methods in the open literature, but this model for VIs and finite deference scheme (FDS) is the first time it has been studied. Within the various numerical techniques accessible for solving Hamiltonian systems, variational integrators distinguish themselves because of their symplectic quality. Here are some of the symplectic properties: symplectic orthogonality, energy conservation, area preservation, and structure preservation. [ABSTRACT FROM AUTHOR]
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- 2024
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34. Abdul Kalam: an exceptional leader.
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Deshpande, S. M.
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KINETIC theory of gases , *COMPUTATIONAL fluid dynamics , *MONTE Carlo method , *SUBSONIC flow , *EULER equations - Abstract
The article "Abdul Kalam: an exceptional leader" in Current Science highlights the exceptional leadership qualities of Bharat Ratna Abdul Kalam in the field of Aerospace Engineering. The author, S. M. Deshpande, shares personal experiences of collaborating with Kalam on various projects, emphasizing his dedication, humility, and eagerness to learn. Kalam's visionary leadership led to the establishment of important initiatives like the Joint Advanced Technology Programme (JATP) and the AR&DB Centre of Excellence in aerospace CFD, showcasing his commitment to collaboration between academia and defense organizations. [Extracted from the article]
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- 2025
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35. Time almost-periodic solutions of the incompressible Euler equations
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Luca Franzoi and Riccardo Montalto
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fluid dynamics ,euler equations ,almost-periodic solutions ,Applied mathematics. Quantitative methods ,T57-57.97 - Abstract
We construct time almost-periodic solutions (global in time) with finite regularity to the incompressible Euler equations on the torus $ \mathbb{T}^d $, with $ d = 3 $ and $ d\in\mathbb{N} $ even.
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- 2024
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36. Authentic fault models and dispersive tsunami simulations for outer-rise normal earthquakes in the southern Kuril Trench.
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Baba, Toshitaka, No, Tetsuo, Obana, Koichiro, Imai, Kentaro, Chikasada, Naotaka, Tanioka, Yuichiro, and Kodaira, Shuichi
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EARTHQUAKE zones , *EULER equations , *HYDROGRAPHIC surveying , *EARTHQUAKES , *TRENCHES , *TSUNAMIS - Abstract
The southern Kuril Trench is one of the most seismically active regions in the world. In this study, marine surveys and observations were performed to construct fault models for possible outer-rise earthquakes. Seismic and seafloor bathymetric surveys indicated that the dip angle of the outer-rise fault was approximately 50°–80°, with a strike that was slightly oblique to the axis of the Kuril Trench. The maximum fault length was estimated to be ~ 260 km. Based on these findings, we proposed 17 fault models, with moment magnitudes ranging from 7.2 to 8.4. To numerically simulate tsunami, we solved two-dimensional dispersive wave and three-dimensional Euler equations using the outer-rise fault models. The results of both simulations yielded identical predictions for tsunami with short-wavelength components, resulting in significant dispersive deformations in the open ocean. We also found that tsunami generated by outer-rise earthquakes were affected by refraction and diffraction because of the source location beyond the trench axis. These findings can improve future predictions of tsunami hazards. [ABSTRACT FROM AUTHOR]
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- 2024
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37. Propagation of logarithmic regularity and inviscid limit for the 2D Euler equations.
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Ciampa, Gennaro, Crippa, Gianluca, and Spirito, Stefano
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LOGARITHMS ,EULER equations ,CAUCHY integrals ,NAVIER-Stokes equations ,MATHEMATICAL models - Abstract
The aim of this note is to study the Cauchy problem for the 2D Euler equations under very low regularity assumptions on the initial datum. We prove propagation of regularity of logarithmic order in the class of weak solutions with L p initial vorticity, provided that p ≥ 4. We also study the inviscid limit from the 2D Navier-Stokes equations for vorticity with logarithmic regularity in the Yudovich class, showing a rate of convergence of order | log ν | − α / 2 with α > 0. [ABSTRACT FROM AUTHOR]
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- 2024
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38. Concentrated solutions with helical symmetry for the 3D Euler equation and rearrangments.
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Cao, Daomin, Fan, Boquan, and Lai, Shanfa
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SYMMETRY , *CURVATURE , *EULER equations - Abstract
In this paper, we study the existence and stability of concentrated traveling-rotating helical vortex for the 3D incompressible Euler equations in an infinite pipe. The solutions are obtained by maximization of the energy over the set of rearrangments of a fixed bounded function with compact support, and tends asymptotically to singular helical vortex filament evolving by the binormal curvature flow. We also show nonlinear stability of maximizers under L p perturbation for p ≥ 2. [ABSTRACT FROM AUTHOR]
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- 2024
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39. Construction of the free-boundary 3D incompressible Euler flow under limited regularity.
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Aydin, Mustafa Sencer, Kukavica, Igor, Ożański, Wojciech S., and Tuffaha, Amjad
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INCOMPRESSIBLE flow , *SURFACE tension , *VORTEX motion , *EULER equations , *NEIGHBORHOODS - Abstract
We consider the three-dimensional Euler equations in a domain with a free boundary with no surface tension. In the Lagrangian setting, we construct a unique local-in-time solution for u 0 ∈ H 2.5 + δ such that the Rayleigh-Taylor condition holds and curl u 0 ∈ H 2 + δ in an arbitrarily small neighborhood of the free boundary. We show that the result is optimal in the sense that H 3 + δ regularity of the Lagrangian deformation near the free boundary can be ensured if and only if the initial vorticity has H 2 + δ regularity near the free boundary. [ABSTRACT FROM AUTHOR]
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- 2024
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40. Analyzing Richtmyer–Meshkov Phenomena Triggered by Forward-Triangular Light Gas Bubbles: A Numerical Perspective.
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Singh, Satyvir and Msmali, Ahmed Hussein
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MACH number , *EULER equations , *SHOCK waves , *GAS flow , *BUBBLES , *IMPACT strength , *GASES - Abstract
In this paper, we present a numerical investigation into elucidating the complex dynamics of Richtmyer–Meshkov (RM) phenomena initiated by the interaction of shock waves with forward-triangular light gas bubbles. The triangular bubble is filled with neon, helium, or hydrogen gas, and is surrounded by nitrogen gas. Three different shock Mach numbers are considered: M s = 1.12 , 1.21 , and 1.41. For the numerical simulations, a two-dimensional system of compressible Euler equations for two-component gas flows is solved by utilizing the high-fidelity explicit modal discontinuous Galerkin technique. For validation, the numerical results are compared with the existing experimental results and are found to be in good agreement. The numerical model explores the impact of the Atwood number on the underlying mechanisms of the shock-induced forward-triangle bubble, encompassing aspects such as flow evolution, wave characteristics, jet formation, generation of vorticity, interface features, and integral diagnostics. Furthermore, the impacts of shock strengths and positive Atwood numbers on the flow evolution are also analyzed. Insights gained from this numerical perspective enhance our understanding of RM phenomena triggered by forward-triangular light gas bubbles, with implications for diverse applications in engineering, astrophysics, and fusion research. [ABSTRACT FROM AUTHOR]
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- 2024
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41. A simple method improving acoustic mode identification capability based on genetic algorithms.
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Bu, Huanxian, Han, Jun, Xiao, Yuqi, and Zhou, Jie
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GENETIC algorithms ,DISCRETE Fourier transforms ,INVERSE problems ,ACOUSTICS ,EULER equations - Abstract
This letter develops a simple approach of duct mode identification and reconstruction based on genetic algorithms, which can extend the azimuthal mode order range compared to the conventional method based on the (spatial) discrete Fourier transform. The underlying principle is reconstructing the dominant mode from the modal identification forward model through optimization by exploiting the sparsity of the mode amplitude vector. The performance is experimentally demonstrated for detections of one and two azimuthal modes under noisy conditions with nondominant modes. Overall, the proposed genetic-algorithm-based framework for solving acoustic inverse problems is beneficial to duct acoustic testing, particularly design evaluations of fan blades and acoustic liners for aeroengines. [ABSTRACT FROM AUTHOR]
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- 2024
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42. Global well-posedness for the 2D Euler-Boussinesq-Bénard equations with critical dissipation.
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Ye, Zhuan
- Subjects
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CAUCHY problem , *EULER equations , *TRANSPORT equation , *EQUATIONS , *CRITICAL temperature - Abstract
This present paper is dedicated to the study of the Cauchy problem of the two-dimensional Euler-Boussinesq-Bénard equations which couple the incompressible Euler equations for the velocity and a transport equation with critical dissipation for the temperature. We show that there is a global unique solution to this model with Yudovich's type data. This settles the global regularity problem which was remarked by Wu and Xue (2012) [44]. [ABSTRACT FROM AUTHOR]
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- 2024
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43. BV solutions to a hyperbolic system of balance laws with logistic growth.
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Chen, Geng and Zeng, Yanni
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EULER-Lagrange equations , *EULER equations , *CAUCHY problem , *SHOCK waves , *CHEMOTAXIS - Abstract
We study BV solutions for a 2 × 2 system of hyperbolic balance laws. We show that when initial data have small total variation on (− ∞ , ∞) and small amplitude, and decay sufficiently fast to a constant equilibrium state as | x | → ∞ , a Cauchy problem (with generic data) has a unique admissible BV solution defined globally in time. Here the solution is admissible in the sense that its shock waves satisfy the Lax entropy condition. We also study asymptotic behavior of solutions. In particular, we obtain a time decay rate for the total variation of the solution, and a convergence rate of the solution to its time asymptotic solution. Our system is a modification of a Keller-Segel type chemotaxis model. Its flux function possesses new features when comparing to the well-known model of Euler equations with damping. This may help to shed light on how to extend the study to a general system of hyperbolic balance laws in the future. [ABSTRACT FROM AUTHOR]
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- 2024
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44. KFVM-WENO: A High-order Accurate Kernel-based Finite Volume Method for Compressible Hydrodynamics.
- Author
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May, Ian C. T. and Lee, Dongwook
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FINITE volume method , *CONSERVATION laws (Mathematics) , *ASTROPHYSICAL fluid dynamics , *HYDRODYNAMICS , *RADIAL basis functions , *EULER equations , *BENCHMARK problems (Computer science) - Abstract
This paper presents a fully multidimensional kernel-based reconstruction scheme for finite volume methods applied to systems of hyperbolic conservation laws, with a particular emphasis on the compressible Euler equations. Nonoscillatory reconstruction is achieved through an adaptive-order weighted essentially nonoscillatory (WENO) method cast into a form suited to multidimensional reconstruction. A kernel-based approach inspired by radial basis functions and Gaussian process modeling, which we call kernel-based finite volume method with WENO, is presented here. This approach allows the creation of a scheme of arbitrary order of accuracy with simply defined multidimensional stencils and substencils. Furthermore, the fully multidimensional nature of the reconstruction allows for a more straightforward extension to higher spatial dimensions and removes the need for complicated boundary conditions on intermediate quantities in modified dimension-by-dimension methods. In addition, a new simple yet effective set of reconstruction variables is introduced, which could be useful in existing schemes with little modification. The proposed scheme is applied to a suite of stringent and informative benchmark problems to demonstrate its efficacy and utility. A highly parallel multi-GPU implementation using Kokkos and the message-passing interface is also provided. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
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45. The inviscid incompressible limit of Kelvin-Helmholtz instability for plasmas.
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Briard, A., Ripoll, J.-F., Michael, A., Grea, B.-J., Peyrichon, G., Cosmides, M., El-Rabii, H., Faganello, M., Merkin, V. G., Sorathia, K. A., Ukhorskiy, A. Y., Lyon, J. G., Retino, A., Bouffetier, V., Ceurvorst, L., Sio, H., Hurricane, O. A., Smalyuk, V. A., Casner, A., and Prajapati, Ram Prasad
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KELVIN-Helmholtz instability ,PLASMA instabilities ,MACH number ,ASTROPHYSICAL jets ,EULER equations ,HELMHOLTZ resonators ,FLUID-structure interaction - Abstract
Introduction: The Kelvin-Helmholtz Instability (KHI) is an interface instability that develops between two fluids or plasmas flowing with a common shear layer. KHI occurs in astrophysical jets, solar atmosphere, solar flows, cometary tails, planetary magnetospheres. Two applications of interest, encompassing both space and fusion applications, drive this study: KHI formation at the outer flanks of the Earth's magnetosphere and KHI growth from non-uniform laser heating in magnetized direct-drive implosion experiments. Here, we study 2D KHI with or without a magnetic field parallel to the flow. We use both the GAMERA code, which solves the compressible Euler equations, and the STRATOSPEC code, which solves the Navier-Stokes equations under the Boussinesq approximation, coupled with the magnetic field dynamics. GAMERA is a global three-dimensional MHD code with high-order reconstruction in arbitrary nonorthogonal curvilinear coordinates, which is developed for a large range of astrophysical applications. STRATOSPEC is a three-dimensional pseudo- spectral code with an accuracy of infinite order (no numerical diffusion). Magnetized KHI is a canonical case for benchmarking hydrocode simulations with extended MHD options. Methods: An objective is to assess whether or not, and under which conditions, the incompressibility hypothesis allows to describe a dynamic compressible system. For comparing both codes, we reach the inviscid incompressible regime, by decreasing the Mach number in GAMERA, and viscosity and diffusion in STRATOSPEC. Here, we specifically investigate both single-mode and multi-mode initial perturbations, either with or without magnetic field parallel to the flow. The method relies on comparisons of the density fields, 1D profiles of physical quantities averaged along the flow direction, and scale-by-scale spectral densities. We also address the triggering, formation and damping of filamentary structures under varying Mach number or Atwood number, with or without a parallel magnetic field. Results: Comparisons show very satisfactory results between the two codes. The vortices dynamics is well reproduced, along with the breaking or damping of small-scale structures. We end with the extraction of growth rates of magnetized KHI from the compressible regime to the incompressible limit in the linear regime assessing the effects of compressibility under increasing magnetic field. Discussion: The observed differences between the two codes are explained either from diffusion or non-Boussinesq effects. [ABSTRACT FROM AUTHOR]
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- 2024
- Full Text
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46. Applications of Symmetry-Enhanced Physics-Informed Neural Networks in High-Pressure Gas Flow Simulations in Pipelines.
- Author
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Alpar, Sultan, Faizulin, Rinat, Tokmukhamedova, Fatima, and Daineko, Yevgeniya
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FLOW simulations , *COMPUTATIONAL fluid dynamics , *GAS dynamics , *EULER equations , *GAS flow , *ARTIFICIAL neural networks - Abstract
This article presents a detailed examination of the methodology and modeling tools utilized to analyze gas flows in pipelines, rooted in the fundamental principles of gas dynamics. The methodology integrates numerical simulations with modern neural network techniques, particularly focusing on the PINN utilizing the continuous symmetry data inherent in PDEs, which is called the symmetry-enhanced Physics-Informed Neural Network. This innovative approach combines artificial neural networks (ANNs) integrating physical equations, which provide enhanced efficiency and accuracy when modeling various complex processes related to physics with a symmetric and asymmetric nature. The presented mathematical model, based on the system of Euler equations, has been carefully implemented using Python language. Verification with analytical solutions ensures the accuracy and reliability of the computations. In this research, a comparative and comprehensive analysis was carried out comparing the outcomes obtained using the symmetry-enhanced PINN method and those from conventional computational fluid dynamics (CFD) approaches. The analysis highlighted the advantages of the symmetry-enhanced PINN method, which produced smoother pressure and velocity fluctuation profiles while reducing the computation time, demonstrating its capacity as a revolutionary modeling tool. The estimated results derived from this study are of paramount importance for ensuring ongoing energy supply reliability and can also be used to create predictive models related to gas behavior in pipelines. The application of modeling techniques for gas flow simulations has the potential to improve the integrity of our energy infrastructure and utilization of gas resources, contributing to advancing our understanding of symmetry principles in nature. However, it is crucial to emphasize that the effectiveness of such models relies on continuous monitoring and frequent updates to ensure alignment with real-world conditions. This research not only contributes to a deeper understanding of compressible gas flows but also underscores the crucial role of advanced modeling methodologies in the sustainable management of gas resources for both current and future generations. The numerical data covered the physics of the process related to the modeling of high-pressure gas flows in pipelines with regard to density, velocity and pressure, where the PINN model was able to outperform the classical CFD method for velocity by 170% and for pressure by 360%, based on L ∞ values. [ABSTRACT FROM AUTHOR]
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- 2024
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47. Numerical Investigation of Supersonic Flow over a Wedge by Solving 2D Euler Equations Utilizing the Steger–Warming Flux Vector Splitting (FVS) Scheme.
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Wolff, Mitch, Abada, Hashim H., and Saad, Hussein Awad Kurdi
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EULER equations , *SUPERSONIC flow , *MACH number , *NUMERICAL calculations , *WEDGES - Abstract
Supersonic flow over a half-angle wedge (θ = 15°) with an upstream Mach number of 2.0 was investigated using 2D Euler equations where sea level conditions were considered. The investigation employed the Steger–Warming flux vector splitting (FVS) method executed in MATLAB 9.13.0 (R2022b) software. The study involved a meticulous comparison between theoretical calculations and numerical results. Particularly, the research emphasized the angle of oblique shock and downstream flow properties. A substantial iteration count of 2000 iteratively refined the outcomes, underscoring the role of advanced computational resources. Validation and comparative assessment were conducted to elucidate the superiority of the Steger–Warming flux vector splitting (FVS) scheme over existing methodologies. This research serves as a link between theoretical rigor and practical applications in high-speed aerospace design, enhancing the efficiency of aircraft components. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
48. Time almost-periodic solutions of the incompressible Euler equations.
- Author
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Franzoi, Luca and Montalto, Riccardo
- Subjects
EULER equations ,TORUS ,FINITE element method ,MATHEMATICAL models ,COMPRESSIBILITY - Abstract
We construct time almost-periodic solutions (global in time) with finite regularity to the incompressible Euler equations on the torus T
d , with d = 3 and d ∈ N even. [ABSTRACT FROM AUTHOR]- Published
- 2024
- Full Text
- View/download PDF
49. Exact spherical vortex-type equilibrium flows in fluids and plasmas
- Author
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Jason M. Keller and Alexei F. Cheviakov
- Subjects
Plasma vortex ,Fluid vortex ,Euler equations ,MHD equations ,Exact solution ,Axial symmetry ,Plasma physics. Ionized gases ,QC717.6-718.8 ,Science - Abstract
The famous Hill’s solution describing a spherical vortex with nested toroidal pressure surfaces, bounded by a sphere, propelling itself in an ideal Eulerian fluid, is re-derived using Galilei symmetry and the Bragg–Hawthorne equations in spherical coordinates. The correspondence between equilibrium Euler equations of fluid dynamics and static magnetohydrodynamic equations is used to derive a generalized vortex type solution that corresponds to dynamic fluid equilibria and static plasma equilibria with a nonzero azimuthal vector field component, satisfying physical boundary conditions. Separation of variables in Bragg–Hawthorne equation in spherical coordinates is used to construct further new fluid and plasma equilibria with nested toroidal flux surfaces, featuring respectively boundary vorticity sheets and current sheets. Finally, the instability of the original Hill’s vortex with respect to certain radial perturbations of the spherical flux surface is proven analytically and illustrated numerically.
- Published
- 2024
- Full Text
- View/download PDF
50. Efficient visual transformer transferring from neural ODE perspective.
- Author
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Niu, Hao, Luo, Fengming, Yuan, Bo, Zhang, Yi, and Wang, Jianyong
- Subjects
- *
IMAGE recognition (Computer vision) , *ORDINARY differential equations , *TRANSFORMER models , *COMPUTER vision , *EULER equations - Abstract
Recently, the Visual Image Transformer (ViT) has revolutionized various domains in computer vision. The transfer of pre‐trained ViT models on large‐scale datasets has proven to be a promising method for downstream tasks. However, traditional transfer methods introduce numerous additional parameters in transformer blocks, posing new challenges in learning downstream tasks. This article proposes an efficient transfer method from the perspective of neural Ordinary Differential Equations (ODEs) to address this issue. On the one hand, the residual connections in the transformer layers can be interpreted as the numerical integration of differential equations. Therefore, the transformer block can be described as two explicit Euler method equations. By dynamically learning the step size in the explicit Euler equation, a highly lightweight method for transferring the transformer block is obtained. On the other hand, a new learnable neural memory ODE block is proposed by taking inspiration from the self‐inhibition mechanism in neural systems. It increases the diversity of dynamical behaviours of the neurons to transfer the head block efficiently and enhances non‐linearity simultaneously. Experimental results in image classification demonstrate that the proposed approach can effectively transfer ViT models and outperform state‐of‐the‐art methods. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
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