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This paper investigates the theoretical implications of applying Darcy's law to premixed flames, a topic of growing interest in research on flame propagation in porous media and confined geometries. A multiple-scale analysis is carried out treating the flame as a hydrodynamic discontinuity in density, viscosity, and permeability. The analysis accounts in particular for the inner structure of the flame. A simple model is derived allowing the original conservation equations to be replaced by Laplace's equation for pressure, applicable on both sides of the flame front, subject to specific conditions across the front. Such model is useful for investigating general problems under confinement including flame instabilities in porous media or Hele-Shaw channels. In this context, two Markstein numbers are identified, for which explicit expressions are provided. In particular, our analysis reveals novel contributions to the local propagation speed arising from discontinuities in the tangential components of velocity and gravitational force, which are permissible in Darcy's flows to leading order, but not in flows obeying Euler or Navier–Stokes equations. [ABSTRACT FROM AUTHOR]

Most engineering tools dealing with detonation waves in condensed explosives are based on the reactive Euler equations, which involve a thermodynamic closure based on temperature and pressure equilibrium conditions. Indeed, the reactant and the detonation products are assumed to evolve in mechanical and thermal equilibrium. Although the assumption of thermal equilibrium is physically questionable, the reactive Euler equations are used for convenience. This choice is supported by several reasons. When considering thermal equilibrium, the assessment of thermal exchanges between the reactant and the detonation products is simplified, as no exchange coefficient needs to be determined. Furthermore, the reactive Euler equations are in conservative form and the shock relations are well-defined. This model appears to be the simplest option for addressing detonations in condensed explosives. However, this simplicity has limitations and conceals a subtle difficulty that can lead to pathological detonations. The present contribution investigates this difficulty and presents a global exothermic condition to preserve exothermic detonations in the frame of temperature–pressure equilibrium flow models. This condition depends on the equations of state only. It is independent of the kinetics used to model the decomposition of the explosive. By meticulously selecting the thermodynamic parameters of the equations of state for the reactant and detonation products, pathological detonations are prevented, thereby maintaining a globally exothermic reaction consistent with the Zeldovich–von Neumann–Döring theory. [ABSTRACT FROM AUTHOR]

In this work, a three-dimensional aerodynamic shape optimization (ASO) framework is established based on the high-order (direct) discontinuous Galerkin (DG/DDG) discretization, which serves as a flow solver for solving compressible Euler/Navier–Stokes equations. The design variables are introduced to represent the shapes via two parameterization approaches, including Hicks–Henne and Free-Form deformation methods. At each loop, the radial basis function mesh deformation technique is employed to redistribute the meshes. Two typical gradient-based optimization methods are employed to update the shapes. One is the Sequential Quadratic Programming method, whose gradients are computed based on the discrete adjoint-based method using finite difference approximation via perturbating the design variables individually. The other is the steepest decent approach, where the gradients are provided by the Simultaneous Perturbation Stochastic Approximation method using finite difference approximation via perturbating the design variables simultaneously and stochastically. These modules work with the DG/DDG flow solver to search for improved shapes in ASO framework. Several airfoil drag minimization experiments involving 2D/3D inviscid/viscous flow are presented to demonstrate the performance of high-order DG/DDG flow solver in ASO, where the drag coefficients can be reduced significantly with the constraints well preserved. [ABSTRACT FROM AUTHOR]

The concentration phenomena in fluid dynamics can be mathematically described by delta-shocks. With the introduction of flux-function, the Riemann problem for the Euler system with Umami Chaplygin gas equation of state is discussed. What Umami Chaplygin gas means is that the fluid obeys the pressure–density relation where the pressure is negative and is a new generalization of Chaplygin gas. The solutions with six kinds of structures are constructed. Unlike the Chaplygin gas, the delta-shock occurs in solutions, even though the system is strictly hyperbolic and two characteristic fields are genuinely nonlinear. The generalized Rankine–Hugoniot relation and entropy condition for delta-shock are clarified. Additionally, the phenomena of concentration and cavitation and the formation of delta-shocks and vacuum states in solutions are identified and analyzed as the Umami Chaplygin gas pressure and flux-function vanish simultaneously. It is proved that as the pressure and flux-function drop to zero, any solution consisting of two shocks tends to the delta-shock solution of the pressureless Euler system, and any solution consisting of two rarefaction waves tends to the vacuum Riemann solution of the pressureless Euler system. Finally, some numerical results exhibiting the processes of formation of delta-shocks and vacuum states are presented. [ABSTRACT FROM AUTHOR]

Efficient initiation of oblique detonation waves (ODWs) is crucial for optimizing the performance of oblique detonation wave engines. A novel approach is proposed for enhancing ODW initiation through expansion waves in this research. Validation of the expansion wave-reinforced initiation method is conducted via numerical simulations employing multi-species reactive Euler equations and a pressure-dependent reaction mechanism. Results demonstrate a significant reduction in the initiation length of ODWs with the addition of an expansion wave ahead of the wedge, contrasting with the absence of detonation wave initiation on a wedge lacking an expansion wave. A theoretical model, based on expansion wave and shock wave relations, along with constant volume combustion theory, elucidates the underlying mechanism of reinforcement. The model reveals that crossing the expansion wave elevates the fluid's Mach number and locally enlarges the flow deflection angle on the wedge surface, without altering the wedge's structure. Furthermore, post-shock temperature increases and pressure decreases compared to the wedge not encountering an expansion wave. The heightened temperature predominantly triggers ODW initiation, thus reinforcing the process. Theoretical analyses indicate the reinforcement's greater efficacy at lower inflow temperatures and lower inflow Mach numbers, suggesting the expansion wave's suitability for initiation in the early flight stages of an aircraft equipped with oblique detonation wave engines. [ABSTRACT FROM AUTHOR]

A fast solution of supersonic flow is one of the crucial challenges in engineering applications of supersonic flight. This article introduces a deep learning framework, the supersonic physics-constrained network (SPC), for the rapid solution of unsteady supersonic flow problems. SPC integrates deep convolutional neural networks with physics-constrained methods based on the Euler equation to derive a new loss function that can accurately calculate the flow fields by considering the spatial and temporal characteristics of the flow fields at the previous moment. Compared to purely data-driven methods, SPC significantly reduces the dependency on training data volume by incorporating physical constraints. Additionally, the training process of SPC is more stable than that of data-driven methods. Taking the classic supersonic forward step flow as an example, SPC can accurately calculate strong discontinuities in the flow fields, while reducing the data volume by approximately 60%. In the generalization test experiment for forward step flow and compression ramp flow, SPC also demonstrates good predictive accuracy and generalization capability under different geometric configurations and inflow conditions. [ABSTRACT FROM AUTHOR]

In this paper, we use the parabolized stability equations (PSEs) to investigate heat effects on supersonic jet screech. The PSE is derived from the linear Euler equations, and the computations are performed on an empirical mean flow profile. Employing PSE, we can examine several important characteristics of the shear-layer instability waves, including the convection velocity, the growth rate, and the location where the instability waves attain the maximal total amplification. Equipped with these knowledge, we further explore their impacts on the jet screech. Specifically, using a newly proposed iteration scheme, we first identify a more suitable convective Mach number to predict the screech frequency in both heated and cold jets. Second, we find that the transition of the screech mode from the axisymmetric to the helical mode may be explained by the shift in the most amplified instability modes. Using this criterion, we can predict a transition Mach number for the mode staging. Third, by assuming that the effective source location is the position where the instability wave attains its maximal amplitude and using the newly obtained convective Mach number, we can predict the screech mode staging in cold and heated jets using Gao's model. The predictions agree well with the experimental data. Finally, we investigate the heat effects on screech amplitude. It is found that compared to cold jets, the difference between the frequency of the most amplified instability wave and the frequency of the jet screech is much bigger in heated jets, which may lead to a lower screech amplitude. [ABSTRACT FROM AUTHOR]

Multiphase rotodynamic pumps are used by the oil and gas industry to transport mixed media in pipelines. The characteristics of gas–liquid–solid flow in such pumps are significantly affected by the rotor–stator axial spacing so that further investigation is required. Based on the Euler multi-fluid model, the Computational Fluid Dynamics simulations were conducted in this study on the gas–liquid–solid multiphase rotodynamic pump at the rotor–stator axial spacings of 8, 10, 12, 14, and 16 mm, respectively. Changes in the pump's characteristics of external, multiphase flow, and pressure fluctuation were systematically analyzed by using ANSYS-CFX. The results showed that, an overall decreasing trend for the efficiency and head of the multiphase rotodynamic pump were demonstrated with increases in the rotor–stator axial spacing from 8 to 16 mm, which can be categorized into plummets I, moderation, and plummets II. As the rotor–stator axial spacing increased, the pressurization decreased from the inlet to outlet of guide vane while the aggregation of gas and solid increased. Additionally, vorticity increased and vortex structure was found to be more significant. As a result, the overall performance of the multiphase rotodynamic pump deteriorated. The pressure fluctuation in the multiphase rotodynamic pump was determined by the rotor–stator interaction and multiphase flow under gas–liquid–solid flow conditions, resulting in a non-positive correlation between the pressure fluctuation and the pump's external and internal flow characteristics. The location of maximum pressure fluctuation in the multiphase rotodynamic pump was changed from the impeller outlet to the guide vane inlet with increases in rotor–stator axial spacing. [ABSTRACT FROM AUTHOR]

With the assistance of deep learning (DL), we present a framework for predicting the turbulent eddy viscosity in unsteady Reynolds-averaged Navier–Stokes (URANS) simulations for particle-laden jet flows. We report a complete workflow from identifying the input flow and particle quantities in the training phase to predicting the flow and particle fields in the testing phase. The framework incorporates a deep neural network model, also known as multi-layer perceptrons, into the momentum equations of the Euler–Lagrangian gas–solid flow system. A data-driven, physics-informed DL approach was employed to predict the modeled turbulent eddy viscosity field, formulated as a function of the instantaneous flow and particle quantities. In the training phase, these regression functions were trained with an existing high-fidelity direct numerical simulation database. In the testing phase, the trained model was then used to predict the instantaneous local eddy viscosity to update the closure term and to solve the URANS equations iteratively. A series of round, turbulent particle-laden jets in a co-flow with various Stokes numbers were assessed, including those beyond the range of conditions employed for training. The proposed DL–URANS model was found to provide enhanced accuracy for predicting both flow and particle quantities when compared with the baseline URANS simulation. [ABSTRACT FROM AUTHOR]

This paper is mainly concerned with the dynamics of strongly nonlinear internal waves in two-dimensional fluids of great depth. A fully nonlinear model for a three-layer fluid of great depth containing topography, a Miyata–Choi–Camassa (MCC)-type system, is developed based on the generalization of the Ablowitz–Fokas–Musslimani global-relation formulation for free-surface water waves. Mode-1 internal solitary waves are numerically found in the MCC-type equation using the Petviashvili iteration technique and in the full Euler equations based on the boundary integral equation method. The comparison between the results validates the broad applicability of the MCC-type system. Mode-2 internal solitary waves are found in the MCC-type equations and are shown to be a type of gap solitary wave. Using the multi-mode internal solitary-wave solutions in the MCC-type equations, we apply the conformal mapping technique to calculate streamlines and particle trajectories. For unsteady simulations, we propose a pseudo-spectral algorithm to handle the time-coupled equations and investigate the generation mechanism of multi-mode internal solitary waves due to the resonance effect of local protrusion on the rigid wall, as well as their collisions when the wall is flat. For flows past protrusion on the rigid wall, the flow speed can be divided into subcritical, transcritical, and supercritical. The shedding of multi-mode internal solitary waves can occur only in the transcritical region of flow speed. We implement the carving of bifurcation curves with inflection to achieve the regional delimitation and, based on this, the interpretation of the generation mechanism from a physical point of view. [ABSTRACT FROM AUTHOR]

The interaction between a shock wave and an interface delineating two gases engenders intricate flow physics, with particular attention drawn to the hydrodynamic instability due to its practical significance. Previous studies have primarily focused on elucidating different wave patterns and instabilities evolution at the interface during the initial phase of shock interaction with cylindrical or spherical bubbles. However, scant literature has shifted its focus toward exploring the long-term morphology of bubbles, especially those characterized by polygonal interfaces. Notably, the detailed examination of shock interaction with a polygonal interface, such as a triangular one with a constant incident angle, remains largely unexplored in existing literature. Recently, the longtime evolution of detailed flow structures across the interface of shock-forward-facing triangular bubbles was captured by Kundu et al. ["A study on dynamics of shock-accelerated forward-facing triangular bubbles at different Atwood numbers," Phys. Fluids 36, 016110 (2024)] through numerical simulation. In this study, the dynamics of a shock-accelerated backward-facing triangular interface containing various gases, namely, Sulfur Hexafluoride, Refrigerant-22, Argon, Neon, and Helium, is studied for a shock Mach number of 1.21. Simulations were performed by solving the two-dimensional Euler equation using low-dissipative advection upwind splitting methods (AUSMD), in conjunction with a derived ninth-order upwind scheme and a four-stage third-order Runge–Kutta scheme for temporal integration. The development of Richtmyer–Meshkov (RM) and Kelvin–Helmholtz (K–H) instabilities at the interface, mixing, and normalized movements of backward-facing triangular bubbles is captured at different Atwood (At) numbers. [ABSTRACT FROM AUTHOR]

Hydrodynamic equations for a one-component plasma are derived as a unification of the Euler equations with long-range Coulomb interaction. By using a variational principle, these equations self-consistently unify thermodynamics, dispersion laws, nonlinear motion, and conservation laws. In the moderate and strong coupling limits, it is argued that these equations work down to the length scale of the interparticle spacing. The use of a variational principle also ensures that closure is achieved self-consistently. Hydrodynamic equations are evaluated in both the Eulerian frame, where the fluid variables depend on the position in the laboratory, and the Lagrangian frame, where they depend on the position in some reference state, such as the initial position. Each frame has its advantages and our final theory combines elements of both. The properties of longitudinal and transverse dispersion laws are calculated for the hydrodynamic equations. A simple step function approximation for the pair distribution function enables simple calculations that reveal the structure of the equations of motion. The obtained dispersion laws are compared to molecular dynamics simulations and the theory of quasilocalized charge approximation. The action, which gives excellent agreement for both longitudinal and transverse dispersion laws for a wide range of coupling strengths, is elucidated. Agreement with numerical experiments shows that such a hydrodynamic approach can be used to accurately describe a one-component plasma at very small length scales comparable to the average interparticle spacing. The validity of this approach suggests considering nonlinear flows and other systems with long-range interactions in the future. [ABSTRACT FROM AUTHOR]

In this work, we enhance the fifth-order Weighted Essentially Non-Oscillatory (WENO) shock-capturing scheme by integrating deep learning techniques. We improve the established WENO algorithm by training a compact neural network to dynamically adjust the smoothness indicators within the WENO scheme. This modification boosts the accuracy of the numerical results, particularly in proximity to abrupt shocks. Notably, our approach eliminates the need for additional post-processing steps, distinguishing it from previous deep learning-based methods. We substantiate the superiority of our new approach through the examination of multiple examples from the literature concerning the two-dimensional Euler equations of gas dynamics. Through a thorough investigation of these test problems, encompassing various shocks and rarefaction waves, our novel technique consistently outperforms the traditional fifth-order WENO scheme. This superiority is especially evident in cases where numerical solutions exhibit excessive diffusion or overshoot around shocks. [ABSTRACT FROM AUTHOR]

The physics-informed neural network (PINN) method is extended to learn and predict compressible steady-state aerodynamic flows with a high Reynolds number. To better learn the thin boundary layer, the sampling distance function and hard boundary condition are explicitly introduced into the input and output layers of the deep neural network, respectively. A gradient weight factor is considered in the loss function to implement the PINN methods based on the Reynolds averaged Navier–Stokes (RANS) and Euler equations, respectively, denoted as PINN–RANS and PINN–Euler. Taking a transonic flow around a cylinder as an example, these PINN methods are first verified for the ability to learn complex flows and then are applied to predict the global flow based on a part of physical data. When predicting the global flow based on velocity data in local key regions, the PINN–RANS method can always accurately predict the global flow field including the boundary layer and wake, while the PINN–Euler method can accurately predict the inviscid region. When predicting the subsonic and transonic flows under different freestream Mach numbers (M a ∞ = 0.3–0.7), the flow fields predicted by both methods avoid the inconsistency with the real physical phenomena of the pure data-driven method. The PINN–RANS method is insufficient in shock identification capabilities. Since the PINN–Euler method does not need the second derivative, the training time of PINN–Euler is only 1/3 times that of PINN–RANS at the same sampling point and deep neural network. [ABSTRACT FROM AUTHOR]

Blood flow through arterial circulation can be characterized by fluid transport in flexible tubes and modeled mathematically using the conservation of mass and momentum. A one-dimensional model for two-layer blood flow with different blood velocities and the same constant density in each layer derived from the Euler equations of gas dynamics by taking the vertical average across each layer. This work presents interactions of elementary waves with a weak discontinuity for the quasilinear 3 × 3 system of conservation laws governing the two-layer blood flow in arteries. Exploiting elementary waves as a single-parameter curve, we study the Riemann solution uniquely and consequently establish the condition on initial data for the existence of a solution to the Riemann problem. Furthermore, we discuss the evolution of weak discontinuity waves and subsequently derive their amplitudes; in what follows, we investigate the interactions of weak discontinuity with contact discontinuity and shocks. Finally, a series of numerical tests have been performed to understand the impact of shock strength and the initial data on the amplitudes of reflected and transmitted waves and the jumps in shock acceleration. [ABSTRACT FROM AUTHOR]

This study presents an innovative implicit–explicit time-stepping algorithm based on a first-order temporal accuracy method, addressing challenges in simulating all-regimes of fluid flows. The algorithm's primary focus is on mitigating stiffness inherent in the density-based "Roe" method, pivotal in finite volume approaches employing unstructured meshes. The objective is to comprehensively evaluate the method's efficiency and robustness, contrasting it with the explicit fourth-order Runge–Kutta method. This evaluation encompasses simulations across a broad spectrum of Mach numbers, including scenarios of incompressible and compressible flow. The scenarios investigated include the Sod Riemann problem to simulate compressible Euler equations, revealing the algorithm's versatility, and the low Mach number Riemann problem to analyze system stiffness in incompressible flow. Additionally, Navier–Stokes equations are employed to study viscous and unsteady flow patterns around stationary cylinders. The study scrutinizes two time-stepping algorithms, emphasizing accuracy, stability, and computational efficiency. The results demonstrate the implicit–explicit Runge–Kutta algorithm's superior accuracy in predicting flow discontinuities in compressible flow. This advantage arises from the semi-implicit nature of the equations, reducing numerical errors. The algorithm significantly enhances accuracy and stability for low Mach number Riemann problems, addressing increasing stiffness as Mach numbers decrease. Notably, the algorithm optimizes computational efficiency for both low Mach number Riemann problems and viscous flows around cylinders, reducing computational costs by 38%–68%. The investigation extends to a two dimensional hypersonic inviscid flow over cylinder and double Mach reflection case, showcasing the method's proficiency in capturing complex and hypersonic flow behavior. Overall, this research advances the understanding of time discretization techniques in computational fluid dynamics, offering an effective approach for handling a wide range of Mach numbers while improving accuracy and efficiency. [ABSTRACT FROM AUTHOR]

The study found that it is difficult to capture the solutions at the shock wave and discontinuity surfaces when solving Euler equations using physics informed neural network. Thus, this paper proposes an improved neural network based on adaptive weights for multi-input high-dimensional features to solve the Euler equations. First, adaptive weights regarding the velocity are added to the control equation of each residual to train the shock wave region better. Then, more residual training points are used in regions with initial time discontinuities to improve the training efficiency. The problem that the sigmoid activation function is more prone to gradient pathologies than tanh in the training process is also analyzed to show that the Euler equations can be better solved using tanh. Numerical experiments verify that even though the solution process becomes complicated, it outperforms the original physics informed neural network in terms of computational efficiency and computational accuracy and can better portray the physical phenomena of Euler equations. [ABSTRACT FROM AUTHOR]

We present Integrated System Model-hydrodynamics (ISM-hydro)—an interface tracking, finite volume code for modeling a shaped implosion of a rotating, initially cylindrical, fluid shell (liner) with a free surface. The code is a novel implementation of the mixed Lagrangian–Eulerian approach, applied to a compressible fluid in an axisymmetric geometry described by cylindrical coordinates (r, ϕ , z). In ISM-hydro, a structured quadrilateral mesh follows fluid elements in the r-direction (radially Lagrangian) and is fixed in the z-direction (axially Eulerian). This approach accurately captures the motion of the liner's free surface, making it an interface tracking method. Using this mesh, we derive a finite volume discretization of the axisymmetric Euler equations for a rotating compressible fluid that has an exact balance of kinetic energy. An extensive comparison between ISM-hydro and the open-source software OpenFOAM is presented; results for different test cases show very good agreement in simulated implosion trajectories and flow fields. ISM-hydro is the purely hydrodynamic component of the Integrated System Model (ISM), a framework developed at General Fusion (GF) for comprehensive predictive modeling of GF's magnetized target fusion (MTF) scheme, where an imploding rotating liquid metal liner compresses a magnetized plasma target to fusion conditions. Among advantages of the code is its speed: a full implosion simulation with a coarse mesh takes on the order of one minute on a single core while preserving high accuracy. This makes ISM-hydro a valuable tool for the design optimization of GF's MTF machines. [ABSTRACT FROM AUTHOR]

The well-known Guderley similarity solution provides a fundamental example of how a spherically converging shock wave can generate amplitude blowup in compressible Euler flow. Recent work has shown that the same phenomenon can occur in continuous flow. In this work, we analyze a different type of continuous similarity flows in which density, velocity, and sound speed all suffer gradient blowup at collapse, while remaining locally bounded. We give examples where, notwithstanding the presence of gradient singularities, no shock wave appears at collapse and the flow is globally continuous. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the limiting behavior of Riemann solutions to the Euler equations of compressible fluid flow for modified Chaplygin gas with the body force as the two parameters tend to zero. The formation of delta shock waves and the vacuum states is identified and analyzed during the process of vanishing pressure in the Riemann solutions. The concentration and cavitation are fundamental and physical phenomena in fluid dynamics, which can be mathematically described by delta shock waves and vacuums, respectively. In this paper, our main objective is to rigorously investigate the formation of delta shock waves and vacuums and observe the concentration and cavitation phenomena. First, the Riemann problem of the Euler equations of compressible fluid flow for the modified Chaplygin gas with the body force is solved. Second, we rigorously confirm that, as the pressure vanishes, any two shock Riemann solution to the Euler equations of compressible fluid flow for the modified Chaplygin gas with the body force tends to a δ-shock solution to the pressureless gas dynamics model with a body force, and the intermediate density between the two shocks tends to a weighted δ-measure that forms the δ-shock; any two-rarefaction-wave Riemann solution to the Euler equations of compressible fluid flow for the modified Chaplygin gas with the body force tends to a solution consisting of four contact discontinuities together with vacuum states with three different virtual velocities in the limiting situation. [ABSTRACT FROM AUTHOR]

Knowledge of water and sediment flow characteristics in tunnels is essential for structural safety and post-disaster rescue operations. In this research, we developed a numerical model based on the Euler–Euler approach to simulate the three-phase flow of air, water, and sediment, aiming to predict the spatiotemporal flow characteristics in tunnels following the inrush. The model assumes that air, water, and sediment constitute a continuous medium through each other. The interaction drag between phases was taken into account. A standard k-ε turbulence model was used to simulate the irregular fluid flow. The spatiotemporal fluid behavior within the tunnel was investigated by analyzing the volume fraction, fluid velocity, and fluid pressure. In addition, the effects of the support condition, the machinery obstruction, and the curve radius on the three-phase flow characteristics were discussed. Numerical simulation results indicate that in the spatial dimension, the volume fractions, velocity, and pressure all display gradient distribution; in the temporal dimension, these three parameters all show phased features. Moreover, fluid behavior is greatly influenced by the support condition, the machinery obstruction, and the curve radius. The results establish a fundamental basis for additional investigations concerning spatiotemporal characteristics prediction of water and sediment inrush. [ABSTRACT FROM AUTHOR]

In this paper, a variant of the improved discrete velocity method (VIDVM) is proposed for flows in the whole Knudsen number regimes. This method retains the advantage of the improved discrete velocity method (IDVM), which calculates numerical fluxes through a self-adaptive strategy by combining the microscopic reconstruction and the macroscopic reconstruction. Like the IDVM, the microscopic reconstruction for VIDVM is also based on the collisionless Boltzmann solver. However, different from IDVM, the macroscopic reconstruction for VIDVM is established on the Euler solver instead of the Navier–Stokes solver. Considering that the Euler solver merely computes the inviscid fluxes while the Navier–Stokes solver additionally calculates the viscous fluxes, the present method could be more efficient than IDVM. To validate the accuracy and efficiency of the present scheme, some benchmark cases from the continuum regime to the free molecular regime are conducted. Results reveal that the present scheme can predict the flow as well as IDVM, but the present solver is more efficient than IDVM. [ABSTRACT FROM AUTHOR]

As first proposed by Madelung in 1926, the analogy between quantum mechanics and hydrodynamics has been known for a long time; however, its potentialities and the possibility of using the characteristic equations of quantum mechanics to simulate the behavior of inviscid fluids have not been thoroughly investigated in the past. In this methodology, the incompressible Euler equations are thus substituted by the Schrödinger equation, turning a quasi-linear Partial Differential Equation into a linear one, an algorithm known in the literature as Incompressible Schrödinger Flow. Previous works on the subject used the Fast Fourier Transform method to solve this problem, obtaining promising results, especially in predicting vortex dynamics; this paper aims to implement this novel approach into a Finite Element framework to find a more general formulation better suited for future application on complex geometries and on test cases closer to real-world applications. Simple case studies are presented in this work to analyze the potentialities of this method: the results obtained confirm that this method could potentially have some advantages over traditional Computational Fluid Dynamics method, especially for what concerns computational savings related to the required time discretization, whilst also introducing new aspects of the algorithm, mainly related to boundary conditions, not addressed in previous works. [ABSTRACT FROM AUTHOR]

This study introduces an efficient method designed for the simulation of compressible multiphase flows associated with explosive detonation, primarily in the context of underwater explosions. The proposed approach integrates three core components: the compressible Euler equations, the level-set equation, and the program burn model. Spatial terms of the compressible Euler equations undergo discretization using a fifth-order accuracy weighted essentially non-oscillation reconstruction, while the third-order total variation diminishing Runge–Kutta scheme manages the temporal terms. The level-set method ensures accurate tracking of the multiphase interface. To detail the transition from solid, non-reactive explosives to gaseous detonation products in the condensed charge's detonation reaction zone, the program burn model based on Zeldovich, von Neumann, Doering theory. The efficacy and accuracy of the incorporated program burn model and the multiphase interface capture method are employed through four benchmark tests, exhibiting excellent agreement with previously published data from alternative numerical methods or commercial software. In conclusion, applying the proposed method to four distinct engineering scenarios facilitates a comprehensive understanding of the inherent dynamics associated with detonation and shock wave generation and propagation. [ABSTRACT FROM AUTHOR]

The complexity of flow physics and the associated hydrodynamic instability arising out of interactions of a shock wave with forward and backward-facing triangular interfaces drew the attention of researchers around the globe. In earlier studies, many researchers focused on the formation of different wave patterns, the development of instabilities at the interface, and the flow morphology during the initial phase of shock wave interacting with light and heavier bubbles. However, limited studies are available in the literature on the interaction of shock with a polygonal interface. Furthermore, it is difficult to capture the complex flow physics of a polygonal interface accelerated by shock waves at later time instants. In the present study, the dynamics of shock-accelerated forward-facing triangular interface containing various gases, namely, sulfur hexafluoride, refrigerant-22, argon, neon, and helium, are examined numerically for a longer time duration for a shock Mach number of 1.21. The simulations were performed by solving two-dimensional Euler equations using a low-dissipative advection upstream splitting method algorithm coupled with a derived ninth-order upwind scheme and a four-stage third-order Runge–Kutta scheme. The numerical results demonstrated the influence of the Atwood number on vorticity generation, bubble deformation, mixing, and the development of Kelvin Helmholtz instabilities on the bubble interface up to long instants, which are not available in the literature. The Fourier spectra of the streamwise kinetic energy showed the distribution of energy in the larger and smaller scale vortical structures. [ABSTRACT FROM AUTHOR]

Most variational principles in classical mechanics are based on the principle of least action, which is only a stationary principle. In contrast, Gauss' principle of least constraint is a true minimum principle. In this paper, we apply Gauss' principle to the mechanics of incompressible flows, thereby discovering the fundamental quantity that Nature minimizes in most flows encountered in everyday life. We show that the magnitude of the pressure gradient over the domain is minimum at every instant of time. We call it the principle of minimum pressure gradient (PMPG). It turns a fluid mechanics problem into a minimization one. We demonstrate this intriguing property by solving four classical problems in fluid mechanics using the PMPG without resorting to Navier–Stokes' equation. In some cases, the PMPG minimization approach is not any more efficient than solving Navier–Stokes'. However, in other cases, it is more insightful and efficient. In fact, the inviscid version of the PMPG allowed solving the long-standing problem of the aerohydrodynamic lift over smooth cylindrical shapes where Euler's equation fails to provide a unique answer. The PMPG transcends Navier–Stokes' equations in its applicability to non-Newtonian fluids with arbitrary constitutive relations and fluids subject to arbitrary forcing (e.g., electromagnetic). [ABSTRACT FROM AUTHOR]

To effectively evaluate the structural responses, it is crucial to possess relevant knowledge regarding the blast load on the structure. The loading characteristics of two columns differ from those of a single column due to complex flow-field interference. The spacing effect on blast loading characteristics of two tandem rigid square columns is examined numerically and experimentally for different center spacing between the columns (L = 1.2B–12B, where B represents the side length of a column). This includes studying drag characteristics, distribution patterns of reflection overpressure and impulse, and understanding the physical mechanism under blast load. The experimental tests use a shock tube device powered by high-pressure gas, while numerical simulations solve Euler equations using computational fluid dynamics techniques. Our findings reveal that spacing cases can be categorized into four situations: small and medium spacings (L/B = 1.2–2 and 2.5–4), where the upstream column exhibits a significant shielding effect on the downstream column, resulting in the reduced drag coefficient for the downstream column; large spacings (L/B = 5–7), where drag coefficient improves but remains lower than that of a single column; superlarge spacings with negligible shielding effect (L/B = 8–12), leading to similar blast loading for the downstream column compared to a single column. [ABSTRACT FROM AUTHOR]

The presence of abrupt depth transitions might trigger strong nonlinear effects on propagating water waves near coastal regions. In this study, the dynamics of nonlinear monochromatic waves over a submerged step representing the abrupt depth transitions are investigated both experimentally and numerically. Within the framework of the free-surface Euler equations, a fully nonlinear potential flow model based on a conformal mapping method is established to investigate the higher harmonics. The numerical method has been well validated with experimental measurements. To analyze the wave nonlinearity at the transitions, the higher harmonics are extracted both in the spatial and time domains. It is shown that abrupt depth transitions enhance the higher harmonic amplitudes in the shallower regions on the step. The effects of the incident wave frequency and height are studied. It is found that the higher harmonics induced by the abrupt depth transitions become more significant with increasing wave steepness. An analysis of the evolution of the skewness and kurtosis demonstrates the high asymmetry of the surface elevation on the upstream junction. The asymmetry shows clear nonlinear effect from the higher harmonics. [ABSTRACT FROM AUTHOR]

Rogue waves are known to be much more common on jet currents. A possible explanation was put forward in Shrira and Slunyaev ["Nonlinear dynamics of trapped waves on jet currents and rogue waves," Phys. Rev. E 89, 041002(R) (2014)] for the waves trapped on current robust long-lived envelope solitary waves localized in both horizontal directions become possible, such wave patterns cannot exist in the absence of the current. In this work, we investigate interactions between envelope solitons of essentially nonlinear trapped waves by means of the direct numerical simulation of the Euler equations. The solitary waves remain localized in both horizontal directions for hundreds of wave periods. We also demonstrate a high efficiency of the developed analytic nonlinear mode theory for description of the long-lived solitary patterns up to remarkably steep waves. We show robustness of the solitons in the course of interactions and the possibility of extreme wave generation as a result of solitons' collisions. Their collisions are shown to be nearly elastic. These robust solitary waves obtained from the Euler equations without weak nonlinearity assumptions are viewed as a plausible model of rogue waves on jet currents. [ABSTRACT FROM AUTHOR]

This paper presents the first numerical evidence of the intermittency routes that exist before and after the occurrence of thermoacoustic instability in a subcritical single-element liquid rocket engine burning liquid kerosene and decomposed hydrogen peroxide with increasing oxidizer inlet temperatures (T). Three-dimensional compressible large eddy simulation algorithms, combined with Euler–Lagrangian frameworks, are employed to model the spray turbulent combustion process in a high-pressure rocket combustor where a one-equation eddy viscosity sub-grid turbulence model and a PaSR sub-grid combustion model are used based on OpenFOAM. After verifying the numerical framework and achieving grid independence, we focus on (i) dynamical transition routes before and after the thermoacoustic regime, (ii) frequency-locking phenomena between acoustic perturbations, vortex dynamics, and combustion heat release, and (iii) the underlying physical mechanisms associated with different dynamical states. The results show that as we increase the oxidizer inlet temperature (700 K ≤ T ≤ 900 K), the system dynamics undergo a transition from a state of combustion noise to a period-1 limit cycle via intermittency. Furthermore, by further increasing the oxidizer inlet temperature (950 K ≤ T ≤ 1450 K), a second bifurcation occurs, causing a transition from a limit cycle state back to a combustion noise state also via intermittency. These bifurcation phenomena are attributed to frequency-locking interactions among pressure fluctuations, combustion heat release, and vortex dynamics. Evidence from combustion flow subsystems including mixture fraction, burning modes, and flame-induced vorticity sources provides additional insights into the complex instability mechanism. [ABSTRACT FROM AUTHOR]

In this work, high-precision numerical simulations of detonations in supersonic hydrogen–oxygen premixed gases with different activation energies are carried out. The open-source program Adaptive Mesh Refinement in Object-Oriented C++ is adopted, and the monotone upstream–centered scheme for conservation laws total variation diminishing numerical scheme is utilized to solve the Euler equations coupled with a one-step, two-component reaction model. The wave structure characteristics of the irregular cellular detonation process are obtained, and its initiation and propagation characteristics under different activation energies are analyzed in depth. The results show that, unlike a regular detonation wave structure, the Mach stem of an irregular detonation wave is prone to bifurcation in a supersonic mixture with high activation energy. In addition to the incident shock wave and the Mach stem structure, a hybrid shock wave structure also appears between the two due to the random generation of weak triple points. Moreover, the leading shock wave intensity of the irregular detonation weakens, resulting in the generation of many unburned jets whose sizes and shapes depend on the triple point type. Although the oscillation amplitude of the irregular detonation is large and its regularity is weak, the detonation wave can achieve approximate dynamic stability in the channel. [ABSTRACT FROM AUTHOR]

Traditional methods of initiating oblique detonation waves (ODWs) using wedges and cones face a fundamental challenge in reconciling the need for rapid initiation with stable combustion, especially at low flight Mach numbers (Ma < 8). This study introduces an innovative initiation configuration involving a truncated cone. By utilizing Euler equations coupled with detailed hydrogen–air chemical reaction models, the wave dynamics induced by the truncated cone configuration are systematically explored. The findings reveal that the truncated cone configuration enables more rapid initiation of ODWs compared to conventional cones, while also preserving improved stability when contrasted with wedge. This behavior can be attributed to the planar flow characteristics in the post-shock field of truncated cone, generated by the upstream wedge-shaped shock, and the Taylor–Maccoll flow characteristics, caused by the downstream conical shock. Furthermore, the study delves into the initiation and morphological changes with respect to the inner radius and angle of the truncated cone. As inner radii or truncated cone angle increase, three initiation wave systems emerge: stable, oscillatory, and detached modes. Analysis of the dynamic variations in pressure and velocity within the induction zone highlights that the upstream oscillation originates from the flow velocity in the induction zone falling below the local Chapman–Jouguet velocity of normal detonation wave (NDW). However, the upstream region of the truncated cone exhibits more pronounced expansion effects, leading to momentum loss, and subsequently, the weakening and even vanishing of the NDW. This prompts the downstream oscillation of the initiation structure, instigating a cyclic oscillation pattern. [ABSTRACT FROM AUTHOR]

The concentration and cavitation are fundamental and physical phenomena in fluid dynamics, which can be mathematically described by delta shock waves and vacuums, respectively. In this paper, we are concerned with the Euler equations of compressible fluid flow when the state equation is governed by the extended Chaplygin gas, an important candidate for describing dark matter and dark energy. Our main objective is to apply the flux-approximation method to rigorously investigate the formation of delta shock waves and vacuums and observe the concentration and cavitation phenomena. First, the Riemann problem of the compressible fluid flow with n + 2 parameters including flux and pressure is solved. Then, two kinds of flux approximation are discussed, that is, both the flux perturbation and pressure tend to zero, or only the flux perturbation vanishes while the extended Chaplygin gas pressure partly tends to the Chaplygin gas pressure. The results indicate that different manners of flux approximation have their respective effects on the formation of delta shock waves. Finally, several numerical results are presented to confirm the theoretical analysis. [ABSTRACT FROM AUTHOR]

The use of classic two-dimensional (2D) shallow water equations (SWE) for flooding simulation in complex urban environments is computationally expensive, due to the need of refined meshes for the representation of obstacles and building. Aiming to reduce the computational burden, a class of sub-grid SWE models, where small-scale building features are preserved on relatively coarse meshes by means of macroscale porosity parameters, has been recently introduced in the literature. Among the other porosity-based models, the single porosity (SP) model is relevant because the corresponding one-dimensional (1D) Riemann problem is the building block for the construction of many porosity-based numerical schemes. Like the Riemann problem connected to mathematical models such as the SWE with variable bed elevation and the 1D Euler equations in contracting pipes, the SP Riemann problem may exhibit multiple solutions for certain initial conditions. This ambiguity can be solved by restoring the microscale information of the 2D SWE model that is lost at the SP macroscale. In the present paper, we disambiguate the solutions' multiplicity by systematically comparing the solution of the SP Riemann problem at local porosity discontinuities with the corresponding 2D SWE numerical solutions in contracting channels. An additional result of this comparison is that the SP Riemann problem should incorporate an adequate amount of head loss when strongly supercritical flows past sudden porosity reductions occur. An approximate Riemann solver, able to pick the physically congruent solution among the alternatives and equipped with the required head loss amount, shows promising results when implemented in a 1D single porosity finite volume scheme. [ABSTRACT FROM AUTHOR]

This study investigates the characteristics of stable and unstable cells and wavefronts of detonation waves propagating in annular channels with different inner radii and channel widths using two-dimensional Euler equations along with a two-step induction-exothermic reaction kinetics. The results reveal that the effect of annular channels on the detonation cell structure depends on both the inner radius and channel width. To quantify this effect, a parameter σ is introduced, representing the ratio of the inner and outer radii of the channel. We have discovered that for values of the parameter σ exceeding a critical value σs, the detonation wavefront demonstrates characteristics similar to those observed in a straight channel scenario. On the contrary, when σ is below σs, the wavefront becomes distorted, potentially leading to Mach reflection as σ decreases further to another critical value σm. Additionally, the interaction among expansion waves induced by the inner walls leads to an augmented induced length and the potential occurrence of localized decoupling of the detonation wave, particularly for unstable detonation waves. However, it is worth noting that the re-initiation of the detonation wave may be triggered by the formation of hotspots resulting from the interaction between transverse shock waves and the detonation wave. This study aims to characterize the propagation characteristics of detonation waves within annular channels, with the objective of providing valuable insights for the design and optimization of annular chamber configurations in systems involving detonation. [ABSTRACT FROM AUTHOR]

The Whitham equation is a model for the evolution of surface waves on shallow water that combines the unidirectional linear dispersion relation of the Euler equations with a weakly nonlinear approximation based on the Korteweg–De Vries equation. We show that large-amplitude, periodic, traveling-wave solutions to the Whitham equation and its higher-order generalization, the cubic Whitham equation, are unstable with respect to the superharmonic instability (i.e., a perturbation with the same period as the solution). The threshold between superharmonic stability and instability occurs at the maxima of the Hamiltonian and L 2 -norm. We examine the onset of wave breaking in traveling-wave solutions subject to the modulational and superharmonic instabilities. We present new instability results for the Euler equations in finite depth and compare them with the Whitham results. We show that the Whitham equation more accurately approximates the wave steepness threshold for the superharmonic instability of the Euler equations than does the cubic Whitham equation. However, the cubic Whitham equation more accurately approximates the wave steepness threshold for the modulational instability of the Euler equations than does the Whitham equation. [ABSTRACT FROM AUTHOR]

A resolution-independent data-driven subgrid-scale model in coarsened fluid descriptions is proposed. The method enables the inclusion of high-fidelity data into the coarsened flow model, thereby enabling accurate simulations also with the coarser representation. The small-scale model is introduced at the level of the Fourier coefficients of the coarsened numerical solution. It is designed to reproduce the kinetic energy spectra observed in high-fidelity data of the same system. The approach is based on a control feedback term reminiscent of continuous data assimilation implemented using nudging (Newtonian relaxation). The method relies solely on the availability of high-fidelity data from a statistically steady state. No assumptions are made regarding the adopted discretization method or the selected coarser resolution. The performance of the method is assessed for the two-dimensional Euler equations on the sphere for coarsening factors of 8 and 16 times. Applying the method at these significantly coarser resolutions yields good results for the mean and variance of the Fourier coefficients and leads to improvements in the empirical probability density functions of the attained vorticity values. Stable and accurate large-scale dynamics can be simulated over long integration times and are illustrated by capturing long-time vortex trajectories. [ABSTRACT FROM AUTHOR]

The study investigates the oblique detonation characteristics in a stoichiometric methane–air mixture employing reactive Euler equations coupled with a detailed chemical reaction model. The analysis evaluates the initiation variation for both the inflow Mach number and the wedge angle. The results show that an increase in the Mach number from M0 = 9 to M0 = 12 changes the oblique shock-to-detonation transition from an abrupt to a smooth type. Furthermore, the distinction between high and low Mach numbers is explored through a comparison of the induction length along the wave surface. Additionally, the transition is affected by changes in wedge angle elevation under high Mach numbers, while a large wedge angle generates a second detonation wave surface due to a strong reflection shock downstream under low Mach numbers. Finally, the initiation length is quantitatively compared across varying inflow Mach numbers and wedge angles, which can benefit future investigations of a methane-fueled oblique detonation engine. [ABSTRACT FROM AUTHOR]

Oscillatory shear flow, performed at small-amplitude, interrogates polymeric liquids in their equilibrium states. The fluid responds in sinusoidal shear stress waves whose amplitude and phase lead depend on the dimensionless frequency (called the Deborah number). By contrast, this same flow field, performed at large-amplitude, probes departures from the equilibrium state, and the fluid responds with shear stress in the form of a Fourier series, whose component amplitudes and phase leads depend on both the dimensionless frequency (called the Deborah number) and the dimensionless shear rate amplitude (called the Weissenberg number). The physics of these departures from equilibrium in an oscillatory shear flow may be explained by (i) chain disentanglement or (ii) motion along the polymer chain axes (called reptation) or (iii) macromolecular orientation. Of these radically different and yet otherwise equally effective approaches, only (iii) allows the macromolecular structure to be varied arbitrary so that the effect of molecular architecture on the rheology can be explored. Though much has been written about a large-amplitude oscillatory shear flow, we understand little about the role of molecular structure on the measured behaviors, and this has limited its usefulness. In this work, we explain the higher harmonics of both the shear stress (first and third), the first normal stress differences (zeroth, second, and fourth), and the second normal stress differences (zeroth and second) arriving at analytical expressions for all three. These expressions, written in dimensionless form, express the dimensionless rheological responses in large-amplitude oscillatory shear flow in terms of the ratio of the two principal macromolecular moments of inertia. To get these expressions, we derive the first five terms of the orientation distribution function, by solving the general diffusion equation in Euler coordinates. We then integrate in phase space with this orientation result to arrive at our expression for the first seven terms of the polymer contribution to the extra stress tensor. From this tensor, we next write down the Fourier coefficients for the shear stress responses, and the normal stress difference responses, in large-amplitude oscillatory shear flow for a suspension of macromolecules sculpted from a rigid bead-rod structure of any arbitrary axisymmetric shape. [ABSTRACT FROM AUTHOR]

Jet flows are ubiquitous in nature and laboratories. For example, helium and argon jets into ambient air are commonly used to produce atmospheric plasma jets. The jets before and after discharge both are typical multicomponent flows. This study reports on the implementation of a numerical solver based on the graphic processing units to model multicomponent mixture gas flows. To this end, two- and three-dimensional Jacobian matrices for the multicomponent Euler equations were obtained to reconstruct numerical fluxes and build a total variation diminishing scheme. The two-dimensional early-stage mass transfer of gas jets was studied for three mixture gases: He/air, Ar/air, and N2/air to numerically verify the steady functioning of the numerical solver despite the high mass fraction gradients. The mass fraction distribution of helium in ambient air exhibited more complex substructures than those of argon and nitrogen in ambient air. Using the watershed method, self-generated bullets were extracted from the mass fraction distributions of the helium jet. The proposed numerical solver implemented in this study is expected to provide a better understanding of gas jet dynamics, and the Jacobian matrices can provide a mathematical foundation for constructing potential higher schemes. [ABSTRACT FROM AUTHOR]

A cell-centered spatiotemporal coupled method is developed to solve the compressible Euler equations. The spatial discretization is performed using an improved weighted essentially non-oscillation scheme, where the Harten–Lax–van Leer–contact approximate Riemann solver is used for computing the numerical fluxes. A two-stage fourth-order scheme is adopted to carry out time advancement for unsteady problems. The proposed method is featured by spatiotemporal coupling time-stepping that can be generalized without using the case-dependent generalized Riemann problem solver. A number of one- and two-dimensional test cases are presented to demonstrate the performance of the proposed method for solving the compressible Euler equations on structured grids. The numerical results indicate that the novel method can achieve relatively large Courant–Friedrichs–Lewy (CFL) number compared to other studies that implement the two-stage fourth-order scheme, and that it is more capable of capturing small-scale flow structures than the Runge–Kutta (RK) method. [ABSTRACT FROM AUTHOR]

In this work, we propose a novel selective discontinuity sensor approach for numerical simulations of the compressible Navier–Stokes equations. Since transformation to characteristic space is already a common approach to reduce high-frequency oscillations during interpolation to cell interfaces, we exploit the characteristic wave structure of the Euler equations to selectively treat the various waves that the equations comprise. The approach uses the Ducros shock sensing criterion to detect and limit oscillations due to shocks while applying a different criterion to detect and limit oscillations due to contact discontinuities. Furthermore, the method is general in the sense that it can be applied to any method that employs characteristic transformation and shock sensors. However, in the present work, we focus on the gradient-based reconstruction family of schemes. A series of inviscid and viscous test cases containing various types of discontinuities are carried out. The proposed method is shown to markedly reduce high-frequency oscillations that arise due to improper treatment of the various discontinuities; i.e., applying the Ducros shock sensor in a flow where a strong contact discontinuity is present. Moreover, the proposed method is shown to predict similar volume-averaged kinetic energy and enstrophy profiles for the Taylor–Green vortex simulation compared to the base Ducros sensor, indicating that it does not introduce unnecessary numerical dissipation when there are no contact discontinuities in the flow. [ABSTRACT FROM AUTHOR]

In this paper, we study the one-dimensional isentropic compressible Euler system for the Chaplygin gas through Lie symmetry analysis. The one-dimensional optimal subalgebras are classified using the adjoint transformation and the invariant functions. We derived several new exact solutions from the optimal subalgebras and investigated the physical behavior of some solutions graphically. Next, a tree of nonlocally related partial differential equations (PDEs) is presented and we classify the nonlocal symmetry of the given system. Futher, some nontrivial exact solutions for the given model are constructed using nonlocal symmetries. Furthermore, using the traveling wave transformation, which is invariant under the symmetry group, we obtain solutions of the nature of peakon-type and kink-type solitons. Then, conservation laws are constructed through the direct multipliers method. Finally, the evolutionary behavior of a C1-wave is investigated using one of the developed solutions. [ABSTRACT FROM AUTHOR]

The study of differential schemes with high accuracy and low dispersion is of great significance for the numerical simulation of aeroacoustics over complex geometries. The midpoint-and-node-to-node explicit finite difference is employed to solve the flux derivatives of the linear Euler equations for improving the robustness. To obtain the numerical flux at the center of the grid element, we adopted a hybrid interpolation method of center and upwind interpolations, combined with a symmetrical conservative metric method, to achieve high-resolution discretization of the acoustic field variables and geometric variables of the structural grid. To suppress spurious oscillations and improve the resolution of discontinuous regions, a family of mapping functions is developed to establish different smoothness indicators and applied to the sixth-order weighted compact nonlinear hybrid scheme (WCNHS), forming a new WCNHS scheme based on piecewise exponential mapping functions (WCNHS-Pe). The approximate dispersion relation shows that the dispersion error and numerical dissipation of WCNHS-Pe are smaller than those of WCNHS with a simple mapping function to the original weights in Jiang and Shu and other mapping function-weighted WCNHS schemes. We have applied various WCNHS schemes to the numerical simulation of the Shu–Osher problem, propagation of Gaussian impulses on two-dimensional wavy grids, sound transmission at discontinuous interfaces, propagation of Gaussian impulses on three-dimensional wavy grids, etc. Numerical results indicate that the WCNHS-Pe scheme has better discontinuity capture capability, higher resolution, and lower dispersion under the same differential stencil, and is suitable for computational aeroacoustics of complex geometries. [ABSTRACT FROM AUTHOR]

The Mach cutoff of sonic boom occurs when shock waves propagate from supersonic to subsonic regions in a stratified atmosphere. In this study, numerical simulations are performed to clarify Mach cutoff behaviors in atmospheric temperature inversion layers, which have not yet been investigated. The two-dimensional Euler equations with a gravitational source term are solved in a horizontally stratified atmosphere. Surface and non-surface temperature inversion layers include three and four supersonic–subsonic mixing layers, respectively. Computations are made to analyze the propagation characteristics of a conventional N-shaped waveform. The results show that multiple upward and downward cutoffs occur owing to atmospheric temperature inversions, with multiple outgoing and evanescent waves, and multiple shock wave focusing. The upward and downward cutoffs act similarly. The positive- and negative-pressure regions are inversed when a cutoff occurs twice; thus, each cutoff shifts a phase by π/2, as expressed in the linear theory of caustics. A waveform transition occurs owing to wave splitting in a cutoff region, in addition to the phase shift. For surface temperature inversion, upward cutoffs make the waves between the cutoff and ground surfaces persist, resulting in rumbling. For non-surface temperature inversion, upward and downward cutoffs occur alternately, and the waves between them persist as well. Therefore, multiple cutoffs in temperature inversion layers play an important role in sonic boom evaluation during low supersonic flight. [ABSTRACT FROM AUTHOR]

A new family of compact vortex models is developed and taken as base vortical flows to numerically study the acoustic scattering by solving the two-dimensional Euler equations in the time domain with high-order accurate finite-difference methods and nonreflecting boundary conditions. The computations of scattered fields with very small amplitude are found to be in excellent agreement with a benchmark provided by previous studies. Simulations for the scattering from a Taylor vortex reveal that the amplitude of the scattered fields is strongly influenced by two dimensionless quantities, the vortex strength Mv based on the maximal velocity of the vortex, and the acoustic length-scale ratio λ / R defined as the acoustic wavelength relative to the vortex core size. To have a deep understanding of the roles played by these two quantities, another significant quantity used for describing quantitatively the total amount of scattering, namely, scattered sound power, is introduced. Thereupon, on the basis of a global analysis of scale effects of these two dimensionless quantities on the scattered sound power, the scattering defined in a physical coordinate system with Mv and λ / R is divided into three domains, long-wave domain, resonance domain, and geometrical-acoustics domain. For each domain, we examine the influence of Mv and λ / R in detail and derive the explicit scaling laws involved in the strength of the scattered field and these two dimensionless quantities separately. Furthermore, the computations for the scattering from a high-order compact vortex are conducted at a wide range of Mv and λ / R and compared with the results from the Taylor vortex in each domain to gain some insights into the acoustic scattering by a compact vortex. [ABSTRACT FROM AUTHOR]

The study is aimed at constructing exact solutions that describe unsteady flows of an ideal fluid with a free boundary. Currently existing examples of solutions of this kind have a linear or quadratic initial field of velocities. The object of the present study is flows with a cubic initial velocity field. Several exact solutions are obtained by using a method based on the complex Hopf equation for the complex velocity. One of the main problems in solving the Euler equations in the domain with a free boundary is to study the positions of singular points because these points can reach the free boundary with time, which may lead to solution destruction. In the present case, singularities can be found explicitly. However, as the initial velocity field is defined by a third-power polynomial, one has to study the Riemann surfaces for the function of complex velocity in order to determine the mutual positions of the singularities and flow domain. It is shown that any initial velocity field defined by a cubic polynomial yields one of seven flows described in the paper with time. It is of interest that there are examples of flows that exist for a finite time and break down when the singularities reach the free boundary. Using a certain modification of the Hopf equation, we obtain a two-parameter family of exact solutions that describe fluid flows with a free boundary. Two examples of this family are considered. In one of them, the solution breaks down within a finite time. The second example is of interest because the motion of a singular point in the fluid leads to the formation of a narrow channel with free boundaries. [ABSTRACT FROM AUTHOR]

We establish the existence of radial self-similar Euler flows in which a continuous incoming wave generates a blowup of primary (undifferentiated) flow variables. A key point is that the solutions have a strictly positive pressure field, in contrast to Guderley's classic construction of converging shock waves. In Guderley's solutions, a converging shock invades a quiescent region at zero pressure (due to vanishing temperature), and the velocity and pressure in its immediate wake become unbounded at the time of collapse. It is reasonable that the lack of upstream counter-pressure is conducive to large speeds, with concomitant large amplitudes. Based on Guderley's original solutions, it is therefore unclear if it is the zero-pressure region that is responsible for blowup. The same applies to self-similar Euler flows describing radial cavity flow. Our results demonstrate that the geometric mechanism of wave focusing is sufficiently strong on its own to drive unbounded growth. We propagate the solution beyond blowup and observe numerically that there are two distinct possibilities depending on the incoming flow: either an expanding spherical shock wave is generated, or the flow propagates in a continuous manner. Focusing on the former case, we show that the resulting flows define global admissible weak solutions to the full, multi-d compressible Euler system. These solutions have the unusual property that the flow is isentropic in each of the two regions separated by the shock. [ABSTRACT FROM AUTHOR]

In this paper, we analyze the Riemann problem for concentration and cavitation phenomena to the isothermal Euler equations for van der Waals gas with dust particles in the presence of flux approximation. By the Riemann problem, we mean that it is an initial value problem for the system of conservation laws supplemented by constant discontinuous initial data involving one breaking. The existence of δ − shock and vacuum state in the Riemann problem for the system under consideration is examined. Further, it is shown that as the flux approximation and pressure vanish, the Riemann solution containing two shock waves to the isothermal Euler equation for van der Waals gas with dust particles converges to δ − shock solution and the Riemann solution containing two rarefaction waves tends to the vacuum state solution of the transport equations. Numerical simulations presenting the formation of δ − shocks and vacuum states for different flux approximations are also shown. [ABSTRACT FROM AUTHOR]

Two phase flows that include phase transition, especially phase creation, with a sharp interface remain a challenging task for numerics. We consider the isothermal Euler equations with phase transition between a liquid and a vapor phase. The phase interface is modeled as a sharp interface and the mass transfer across the phase boundary is modeled by a kinetic relation. Existence and uniqueness results were proven in the work by Hantke and Thein ["A general existence result for isothermal two-phase flows with phase transition," J. Hyperbolic Differ. Equations 16, 595–637 (2019)]. Using sharp interfaces for simulating nucleation and cavitation results in the grid containing tiny cells that are several orders of magnitude smaller than the remaining grid cells. This forces explicit time stepping schemes to take tiny time steps on these cells. As a remedy, we suggest an explicit implicit domain splitting where the majority of the grid cells is treated explicitly and only the neighborhood of the tiny cells is treated implicitly. We use dual time stepping to solve the resulting small implicit systems. Our numerical results indicate that the new scheme is robust and provides significant speed-up compared to a fully explicit treatment. [ABSTRACT FROM AUTHOR]