Search

A calibration method for determining the parameter values of reactive flow models (RFMs) required for hydrodynamic simulations is introduced, especially for predicting steady-state detonation based on a unified system of two reduced order models, detonation shock dynamics (DSD) and streamline theory (SLM). This method allows the fast calibration of RFM parameters by utilizing parameter sensitivities to fit the characteristics of different experimental data and fast prediction of either shock-curvature relations or diameter effect curves. It can provide good initial seed approximations to parameter values that can be used in the refinement of larger optimization systems that include most of the required physical features for predicting detonation performance in new high explosive. In this paper we describe essential mathematical formulations and validate the models by comparing calibration results between the reduced models and standard hydrocodes that fit diameter effect curves for a typical explosive through a kinetic model and non-ideal equations of state (EOS). In addition, although we believe that simple first-order reductions of each model are sufficient for calibrating RFMs, we also present higher-order approximations of these models and discuss their feasibility. [ABSTRACT FROM AUTHOR]

Two approaches are considered for modeling the speed of detonation in a finite diameter rate stick. One approach is a simulation using a shock-fit solution to the reactive Euler equations. The second approach uses reactive flow models to solve for a set of detonation speeds at fixed curvatures and uses Detonation Shock Dynamics (DSD) to solve for the propagation speed in the rate stick. The DSD approach is much faster than the shock-fit approach but fails to make good predictions for small diameter rate sticks. This paper describes both methods and identifies a dimensionless parameter where the accuracy of the DSD method decreases compared to the shock-fit method. This shows the possibility of a hybrid method, using both techniques, to provide more computationally efficient predictions of rate stick speeds for reactive burn model calibration and uncertainty quantification studies. [ABSTRACT FROM AUTHOR]

The present study aimed to design a subsonic wind tunnel and compare the numerical and experimental results to ensure the accuracy of the design that has been manufactured after the simulation process. The Euler equations of the two-dimensional inviscid flow were solved using a finite volume approach by utilizing an algorithm developed in MATLAB. The values of velocity in the x direction (u), velocity in the y direction (v), static and stagnation pressure, and density of the flow were computed at each point of a (100 X 32) mesh with a time step of 0.002 X 10−7 for 1000 iterations. The mass flow rate FMR value of one, the uniformity of the flow in the test section, which is obvious in the fluid properties contours, the pressure value of 105 N/m2 that has been constant at inlet and outlet, and the good agreement of numerical and experimental results between pressure and velocity variations along the centerline of the subsonic wind tunnel are all indicators of the accuracy and computation efficiency of the analysis method that has been used. [ABSTRACT FROM AUTHOR]

In this paper compressible two-phase flow is investigated in the relativistic framework. The mixture variables are defined in terms of the relativistic variables rather than their classical counterparts. We consider the case of a single phase, common pressure as well as a mixture pressure. The equations are shown to reduce to their respective non-relativistic and single-phase limits for slow speeds and negligible pressure contribution. [ABSTRACT FROM AUTHOR]

We propose an asymptotic preserving (AP) Implicit-Explicit (ImEx) scheme for the hyperbolic heat equation in the diffusive regime. This scheme is second order in time and space and l∞-stabile under relatively low constraints on the time step, and without requiring the use slope limiters. The construction exploits a formalism developed in a previous work and, compared to it, leads to a simpler implementation but it loses uniform accuracy on paper. Stability and accuracy are verified on numerical examples, and even uniform accuracy is obtained on those. Finally, we discuss extensions of this method to the non linear case of isothermal Euler equations with friction. [ABSTRACT FROM AUTHOR]

In this paper, we study traveling waves with elastic and inelastic interactions in a low order of approximation. The waves are derived in quadratic or linear order of approximation from the two-dimensional Euler equations. A new type of inelastic interaction that is closely related to numerical study observations of the Euler equations is obtained in a linear order. [ABSTRACT FROM AUTHOR]

The aim of this study is to analyze synchronisation and coordination of purkinje fibre cells (PFC) with ventricular myocardium. In that particular focus on Sodium (Na+) concentration is responsible for Action potential (AP) generation. Here this paper is based on the model of Humanendocardial cell by Aslandi (ALD). The ALD model data is modified based on the experimental data of Han, describing the properties of Na+ currents in human PFC. Euler integration protocol is used to analyze the human PFC model for different concentration failure conditions in the same group of 100 samples by keeping threshold 0.05, G power 80%, confidence interval 95% and enrolment ratio 1. The normal AP is -53.04 mV for normal Extracellular Na+ Concentration (Na+o =140mM) and for different increasing levels of Na+o in PFC like (10%=154mM, 25%=175mM, 50%=210mM, 100%=280mM) having AP as (10%= -52.56mV, 25%= -56.26mV, 50%= -44.56mV, 100%= -39.39mV). AP for different decreasing levels of Na+o in PFC like (10%= 126mM, 25%=105mM, 50%=70mM, 100%=0.1mM) having (10%= -51.98mV, 25%= -72.02mV, 50%= -75.75mV, 100%= -75.35mV). AP for different increasing level of intracellular Na+ concentration (Na+i)in PFC like (10%=8.8mM, 25%=10mM, 50%=12mM, 100%=16mM) having AP (10%=-53.08mV, 25%=-70.58mV, 50%=-73.47mV, 100%=-76.76mV), AP for different decreasing levels of Na+i in PFC like (10%=7.2mM, 25%=6mM, 50%=4mM, 100%=0.1mM) having (10%=-46.46mV, 25%=34.92mV, 50%=-28.98mV, 100%= -25.14mV). Similarly its mean value of fast Na current (INa in Pico Ampere (pA)) varied according to different deviant conditions. The results of normal and abnormal concentration of Na+ in intracellular and extracellular PFC affects the depolarization phase due to prolonged total cycle length of AP which leads to cardiac failure. [ABSTRACT FROM AUTHOR]

The Fornberg-Whitham partial differential equation of the third order was proposed to replace the general Euler equations for water waves and as it had been found at least for some cases especially for short wavelengths it copes the problem successfully. Since the very beginning some attempts were undertaken to find different solutions of this equation. The Lie group approach is used in this work to reduce the Fornberg-Whitham equation to an ordinary differential equation of the second order. Invariant solutions of the latter equation are solved numerically. [ABSTRACT FROM AUTHOR]

A recent study of low-dissipation shock-capturing scheme [Fu et al., Journal of Computational Physics 305 (2016): 333-359] proposed a nonlinear sharp selection function to remove the contributions of candidate stencils containing discontinuities from the final reconstruction. In this paper, we train a neural network to replace this empirical level nonlinear selection function in the six-order TENO6-opt scheme. The performance and robustness of the neuron-based six-point scheme are demonstrated with the advection function and 1D Euler equations. [ABSTRACT FROM AUTHOR]

The present study reports a detailed assessment of various reconstruction schemes required for Euler Equation solvers using the open-source CFD platform, OpenFOAM. Three different inviscid flux formulations of Kurganov-Tadmor, Kurganov-Noelle-Petrova, and AUSM+-up of Liou are used to access their performance. The reconstruction of flux at a finite volume cell interface is facilitated by Total Variation Diminishing (TVD) schemes such as Van Leer, QUICK, Min Mod, or Weighted Essentially Non-Oscillatory of arbitrary order (WENO). The most accurate yet stable inviscid flux formulation with a suitable reconstruction scheme is recommended by performing computations on a standard benchmark problem of oblique shock reflection and accessing the accuracy of all the aforementioned flux formulation and reconstruction schemes. [ABSTRACT FROM AUTHOR]

In the cleaners of raw cotton from small trash impurities, the main cleaning module consists of a transporting mean with a different design of the headset, which provides loosening and transportation of the cotton flow along the mesh surface, along which the process of separating trash impurities takes place. In practice, a set of such modules in various installation variations forms the overall profile of the cleaner. It was revealed that the impact interaction of cotton flyings significantly affects the quality indicators of seeds and fibrous mass. Also, in the modules there are various other factors that contribute to the effective release of small trash impurities, such as air flows and the presence of strips, which affect the process of cleaning cotton. To search for technical solutions to these problems in a theoretical way, the report presents a mathematical model for the separation of trash from the stationary flow of raw cotton mass in the cleaning zone, which is the area between the space of the system of rotating spikes and the mesh surface. A one-dimensional Euler equation is compiled with respect to the pressure, the velocity of the density of a moving stream of raw cotton, where the law of conservation of the mass of the stream and the equation of state representing the relationship between the pressure and density are used. After determining the distribution field of the density of raw cotton in each section of the cleaning zone, the model of A.G. Sevostyanov was used, which describes the release of trash impurities from the mass of raw cotton under the impact of spikes. The graphical dependences of the distribution of the amount of separated trash impurities from the cotton flow along the arc were obtained. [ABSTRACT FROM AUTHOR]

Backward Euler for two dimensional Sobolev equation is discussed in this article. We begin by obtaining some basic a priori estimates for the semi-discrete scheme and for the backward Euler approximation. It is proven that these estimations for the discrete scheme are valid uniformly in time using the discrete Gronwall's Lemma. In addition, the presence of a discrete global attractor is established. Furthermore, optimal a priori error bounds are determined, which are time dependent exponentially. Under the uniqueness condition, these error estimates are demonstrated to be uniform in time. Finally, we establish several numerical examples that validate our theoretical approach. [ABSTRACT FROM AUTHOR]

Numerical modeling of supersonic flow around solid bodies is a complex task due to the possibility of nonphysical instabilities that can affect the solution. In this paper, we propose a new hybrid numerical flux for calculating the fluxes of the Euler part of the Navier-Stokes system of equations. This flux avoids the occurrence of instability and maintains high accuracy on shock waves and boundary layers. This flux is a combination of Godunov's numerical flow and Rusanov-Lax-Friedrichs numerical flow. Numerical simulation of supersonic flow around a cruise missile Tomahawk has been carried out. [ABSTRACT FROM AUTHOR]

Since the advent of computational simulations for understanding physical phenomena, there has been a constant effort to develop better, more efficient and more accurate numerical schemes. In this regard, the Harten's Total Variation Diminishing (TVD) Scheme is known to give solutions of higher accuracy even with coarse grids. In the present work, suitability of this scheme is assessed for a hypersonic flow problem. Explicit TVD scheme of first and second order accuracy with entropy fix is utilized to construct an in-house 2D solver to solve the Euler Equations of fluid flow in both the Eulerian and Lagrangian coordinate systems. Min-mod limiter function was utilized to avoid spurring oscillations while implanting the second-order method. The results are first validated for supersonic flow problem followed by assessments of suitability of the scheme for hypersonic flows with three inlet Mach numbers (M=5, 6 and 8). It is found that the scheme was highly effective for the supersonic flow case. However, for hypersonic flow problems, solutions couldn't be obtained for inlet M=8 with the 2nd order scheme. This could be attributed by a fact that there are sudden Jacobian transformations due to local mesh density. [ABSTRACT FROM AUTHOR]

In this paper, the two-dimensional incompressible rotating and stratified equations are analytically investigated. We examine rotating and stratified Euler equations and the normal Euler equations with the self-similar Ansatz. The analytic solutions are available for our all models for velocity, density and pressure fields. In general, they have a rich mathematical structure involving compound power-law dependent functions. Some of them show unphysical explosive properties, others are physically acceptable and have finite numerical values with power law decays. For a better transparency we present some figures for the most complicated velocity and pressure fields. [ABSTRACT FROM AUTHOR]

In this paper, a collocation technique is employed with the help of Euler polynomials to obtain the numerical solution of singular weakly linear Volterra- integro-differential equations. The main feature of this technique is that approximate solutions will be obtained in the form of algebraic equations. Error analysis is shown in the Euler series solution of weakly linear Volterra- integro-differential equations. At last, few numerical problems are solved with the help of the presented technique to present the high accuracy and excellent behavior of the suggested technique in comparison with some other well-known methods. [ABSTRACT FROM AUTHOR]

It is well known that numerical simulations of high-speed reacting viscous flows, in the framework of state-to-state (STS) formulations, are often prohibitively computationally expensive. In this work, we investigate the possibility of using machine learning algorithms (MLAs) for STS approaches in order to alleviate such issue. As a first step in this direction, we assessed the potential of data-driven regression models based on machine learning to predict the relaxation terms which appear in the r.h.s. of the Euler system of equations for a one-dimensional reacting shock flow in the STS approach for a N2/N binary mixture. Results show that by appropriately choosing the MLA regressor and opportunely tuning the hyperparameters it is possible to achieve accurate predictions compared to the full-scale STS simulation in significantly shorter times. [ABSTRACT FROM AUTHOR]

The paper considers a method for determining the impedance of acoustic liner sample based on numerical simulation of physical processes in resonators at a grazing incidence of a sound wave. The test section of a grazing incidence impedance tube (GIIT) and a model of acoustic liner sample, consisting of 7 honeycomb cells with a depth of 27 mm and 11.9% porous perforate facesheet is simulated. Numerical simulation is based on direct solution of the non-stationary compressible Navier-Stokes equations in a three-dimensional formulation. The pressure-time signals recorded in numerical simulation are processed by the Dean method. The obtained impedance is compared with that educed on full-scale experiment data for a single-layer acoustic liner sample, consisting of 72 honeycomb cells of a similar design. The impedance eduction is performed by minimizing the residual functional, which is the total discrepancy between the calculated and experimental acoustic pressure on the wall of the GIIT. The calculated values of the acoustic pressure are determined by the numerical solution of the Helmholtz equation and the linearized Euler equations for a duct with an impedance wall. [ABSTRACT FROM AUTHOR]

The flow in 2D channels of variable cross-section was studied numerically. The channels contain bodies that split the channels into narrow ones. Solutions of Euler's equations are obtained using the finite-volume solver of the Ansys CFX software package. A set of solutions is found. These solutions depend on the input Mach number and on the initial condition. Numerical simulations show a significant hysteresis in the drag coefficient of bodies in the channel relative to the supersonic Mach number set at the inlet. In a certain range of the inlet Mach number, there are asymmetric solutions of the equations. [ABSTRACT FROM AUTHOR]

In the current work the preliminary results of numerical simulations of detonation wave propagation with detailed hy- drocarbon chemical mechanisms are presented. 1D and 2D cases are investigated. All simulations are conducted using an in-home code solving the chemically reacting Euler equations on supercomputers with GPUs. Four chemical models are considered: AFRL model, Singh–Jachimowski model, Varatharajan–Williams model and GRI-Mech 3.0 model. Due to complexity of GRI-Mech 3.0 model it is not used for 2D numerical simulations of detonation wave propagation. For all chemical models the Chapman-Jouguet velocity is obtained, the ignition delay is determined and the Zeldovich–Neumann–Doering solution is obtained in order to compare how suitable they are for numerical simulations of detonations. The 2D Euler equations are solved for an ethylene/oxygen/nitrogen mixture using high-order shock-capturing TVD schemes and a finite-rate chemistry solver. The sizes of detonation cells obtained with different models are compared with each other and experimental data. [ABSTRACT FROM AUTHOR]

The precessional motion of a fullerene molecule during deformation of a section of a fullerite crystal was studied. The dynamic characteristics of the C60 fullerene molecule inside the crystal fragment were determined using the apparatus of classical mechanics using the model of atom-atomic interactions, the dynamic Euler equations, and the equation of the dynamics of translational motion. For numerical implementation, the Runge-Kutta method of the fourth order of accuracy is used. As a result of the performed numerical experiments, the effect of the rotation frequency of the fullerene molecule and the direction of deformation of the fullerite fragment on the ability of the C60 molecule to withstand the external forces was studied. [ABSTRACT FROM AUTHOR]

Nonstandard finite difference (NSFD) methods provide an efficient way to numerically solve many problems in engineering and science. NSFD methods also provide many advantages over classical techniques, such as preserving important physical properties of the corresponding problem. In recent years, some NSFD methods were constructed that are elementary stable but only first order accurate. In this work, we propose and analyze a new non-standard finite difference method which is both elementary stable and of second order accuracy. In addition, we validate the new method using a set of numerical simulations. [ABSTRACT FROM AUTHOR]

This study focuses on the preconditioning methods for adjoint equations of the compressible Euler equations. A strategy to find the adjoint forms of a preconditioning matrix and an artificial dissipation for the Roe’s approximate Riemann solver is proposed. Preconditioned adjoint equations are solved using the implicit boundary condition techniques in an unstructured grid system. The convergence histories of the proposed preconditioning methods will be compared for several well-known problems. [ABSTRACT FROM AUTHOR]

A time consistent preconditioning method for gas-liquid two-phase flows is proposed and applied to the two-phase shock tube problem. A finite-difference 4th-order Runge-Kutta method and a Roe-type flux splitting method with the MUSCL TYD scheme are employed. The artificial viscous terms in the flux splitting are modified by using the preconditioner to enhance the stability of computation for compressible and incompressible flow with arbitrary Mach numbers. A homogeneous equilibrium gas-liquid two-phase model taken account of the compressibility of mixed media is used. Therefore, the present method permits simple treatment of the whole gas-liquid two-phase flow field including wave propagation, large density changes and incompressible flow characteristics at the low Mach number. By this method, a Riemann problem for the one-dimensional Euler equations was computed and confirmed the applicability to the unsteady and arbitrary Mach number flow problems. Detailed observations of shock and expansion wave propagations through the gas-liquid two-phase media and comparisons of predicted results with exact solutions are provided and discussed. [ABSTRACT FROM AUTHOR]

In this study, the interaction between a propagating cellular detonation in stoichiometric 2H2/O2 and 2H2/O2/2Ar mixtures with different bluff bodies is investigated computationally. Numerical simulations are performed based on the two-dimensional reactive Euler equations with detailed chemistry models. A finite-volume package AMROC - an opensource code based on the structured adaptive mesh refinement (SAMR) technique - is used for the computations using both a 2nd order accurate, shock-capturing MUSCL-TVD finite volume method and a first-order accurate Godunov splitting method to handle the reaction source term. Adaptive mesh refinement (AMR) is employed to dynamically increase the resolution of a simulation in regions around shocks and reaction fronts. The present numerical results are compared with the recent experimental measurement. The detonation cell evolution, different regions downstream after the interaction, and the effect of obstacle scale and combustible mixture sensitivity are analyzed and discussed. [ABSTRACT FROM AUTHOR]

In the paper, a physical and mathematical model is proposed, and the corresponding numerical algorithm is developed to calculate the shock-wave flow, generated by the explosion of a complex-shaped cloud. As an example, we simulate the atmosphere blast of the propylene-air mixture above a flat horizontal surface. The cloud has a shape of tor, which axis makes the 30 degrees angle with the normal to the substrate. Similar clouds can be formed during powerful emergency jet emissions of explosive gas into the atmosphere. Numerical simulation of the problem based on solving of a system of 3D transient Euler equations, supplemented by the transport equations for a two-component gas medium and the energy conservation equation. Gas explosion assumed to be instantaneous. After the explosion, the reaction products are supposed to be in a "frozen" state, and their thermodynamic parameters are calculated by explicit algebraic formulas depending on pressure and temperature. Based on the results of numerical simulation, a complex shock-wave structure of the flow and dynamics of pressure profile in the vicinity of the explosion zone and near the horizontal surface are obtained. Flow picture includes two non-concentric ring shocks and internal expansion wave. Based on the computation results, the complex wave structure is analyzed, and pressure loads on the substrate are evaluated. [ABSTRACT FROM AUTHOR]

A theoretical description of the temperature of a fullerite molecular crystal based on C60 ions is given in the framework of a mathematical model in which the Euler equations for projections of angular velocities and rotation angles are used to describe the rotation of molecules, and translational displacements are determined by the Hamilton equations of motion for the centers of mass of fullerenes. Vibrations of carbon atoms are determined in the REBO force field, and translational displacements by the potential LJ. The performed calculations show that rotations are realized in the form of angular vibrations with subsequent reorientation of the rotational axes. The calculations showed that it is possible to achieve an uneven distribution of energy among groups of motions, which makes it possible to accumulate energy on rotational degrees of freedom. [ABSTRACT FROM AUTHOR]

The paper is focused on the study of supersonic gas flows with suspended particles past blunt bodies. Flows with particles of two different sizes are considered. The main feature of the issue under investigation is the significant difference of characteristic scales for carrying and dispersed phases. The study is based on a complex mathematical model of the two-phase flow. The model combines Eulerian description for the gas phase and Lagrangian description for the dispersed phase. The carrying phase dynamics is governed by modified Euler equations, taking into consideration the particle-gas interaction. To account for inter-particle collisions and interaction of particles with the body surface, direct numerical simulation is used. The results of mathematical modeling for a supersonic flow with binary particle admixture around a sphere are presented. The focus is on the analysis of the effects related to the influence of the interaction between particles of different size on the energy flux from the dispersed phase to the sphere surface. The results show that energy fluxes from the individual dispersed fractions to the body surface are nonlinear functions of the particle volume concentrations. Collisions between particles of different size give significant rise to the impact of smaller particles. At the same time, the total energy flux from the dispersed phase to the body surface changes almost linearly with the concentration of individual fractions. This allows using the results of monodispersed flow calculation for modeling of polydispersed flows. [ABSTRACT FROM AUTHOR]

The granular flow induced by high-speed impact was experimentally and numerically investigated. A sheet of free-falling small glass beads was formed in the test chamber at low pressure. A spherical projectile or a slender puff of particle cloud launched by the ballistic range collided with the particle sheet in the in-plane direction to obtain a quasi-two- dimensional situation. The observation by the high-speed camera revealed that the shock-layer-like compressed zone and the void zone were formed on the forward side and the backward side, respectively. To describe such phenomena in the framework of the continuum fluid dynamics, the compressible and non-expanding (CNE) fluid model was applied and the two-dimensional Euler equations were numerically solved by the finite volume method with the Riemann solver formulated for the CNE fluid model. Finding an appropriate set of the parameters in the equation of state, qualitatively good agreement was obtained between the experimental and the computational results. [ABSTRACT FROM AUTHOR]

Shock wave structure in carbon dioxide is studied on the basis of several continuum models and compared to the solution obtained using the kinetic approach. The problem is solved in the frame of one- and two-temperature Euler equations as well as Navier–Stokes equations accounting for the bulk viscosity. The Rankine-Hugoniot relations with constant specific heat ratio fail to predict accurately the final equilibrium state in polyatomic gases. A good qualitative agreement of the solutions obtained using the continuum and kinetic approaches is shown. Taking into account the bulk viscosity leads to a considerable increase in the shock wave width; its variation in a flow modifies the profiles of gas-dynamic parameters. In the multi-temperature approach, solving the Euler equations coupled to the relaxation equation for the vibrational energy provides the results similar to those obtained within the kinetic approach taking into account the effect of bulk viscosity. [ABSTRACT FROM AUTHOR]

Shocks describe a phenomenon which in Fluid Dynamics arises as discontinuties which are in a mathematical sense due to the hyperbolic nature of the underlying system (Euler equations). The shock data (speed, jump conditions) follow from the conservation laws and are prescribed by the Rankine-Hugoniot conditions. In Rarefied Gas Dynamics, shocks do not occur as discontinuities, but as certain variations of the moments driven by a specific algebraic mode related to the collision operator. The knowledge of the precise shock data is important in a number of situations, e.g. for the formulation of well-posed boundary value problems, the numerical coupling of different models, etc. The paper is concerned with the relation between the shock data and the choice of (discrete) models. In particular it works out the explicit dependence of shock speed and jump conditions on the velocity grid, and compares discrete models with their classical continuous counterparts. The results are generalized to gas mixtures. [ABSTRACT FROM AUTHOR]

In the present work a computer code HyCFS-R for numerical simulation of chemically reacting compressible flows on hybrid CPU/GPU supercomputers is developed. It solves unsteady Euler equations for multispecies chemically reacting flows in general curvilinear coordinates using shock-capturing TVD schemes. The developed code is verified by comparing results of numerical simulation with the solutions obtained using ANSYS Fluent software coupled with the user-defined functions for taking into account the thermo-chemical non-equilibrium. [ABSTRACT FROM AUTHOR]

In this paper we review the problem of numerically solving the relativistic Euler gas dynamic equations, comparing results obtained from Riemann free methods and Approximate Riemann Solvers, namely the FORCE and TVD-SLIC methods in the former case and the Flux Vector Splitting and HLL methods in the latter. The test cases of the weak and strong blast waves are considered in rectangular Minkowski, spherical Minkowski and Schwarzschild space-times. Results for each numerical method are reported and compared. [ABSTRACT FROM AUTHOR]

In this study, the deflagration-to-detonation transition from the interaction of a shock wave with multiple laminar flame kernels is analyzed computationally. For comparison, both Euler equations and Navier-Stokes equations including the effects of viscosity, thermal conduction and molecular diffusion for an acetylene–air mixture model with a single-gas approximation are solved numerically to identify the dominant mechanism on the transition process. A finite-volume operating splitting scheme based on the 2nd order Godunov-type, Weighted Average Flux (WAF) method with an approximate HLLC Riemann Solver and second-order finite differences for the Navier-Stokes fluxes evaluation are used in the present computation. Adaptive mesh refinement (AMR) is employed to dynamically increase the resolution of a simulation in regions of interest around shocks, flame fronts and regions of large gradients in density using a hierarchical grid structure. The simulation results show that repeated shock–multiple flames and shock-boundary interactions lead to the acceleration of the original shock into unreacted material near the wall and subsequently the development of a hotspot explosion center. The Richtmyer-Meshkov instability caused by the interaction of the shock with subsequent flames also generates and maintains a highly turbulent flame brush. In the absence of physical diffusion in the Euler simulation, the enhanced burning rate of the turbulent flame brush is suppressed. Nevertheless, the intense flow fluctuations generated by the interactions of shocks, boundary and flames create the conditions under which deflagration-to-detonation can potentially occur at later times. A numerical study is also carried out to verify the effect of numerical grid resolution. [ABSTRACT FROM AUTHOR]

A numerical implementation of characteristic boundary conditions for Euler and Navier-Stokes equations is presented. The method combines the specified boundary conditions and the outgoing characteristic variables according to the wave propagation directions. In the general case, the proposed boundary conditions update the primitive variables by solving a small system of linear equations (4×4 in 2D, 5×5 in 3D) at each boundary point/cell. The method can be used for both preconditioned and non-preconditioned equations. For a perfect gas without preconditioning, a closed analytical solution is provided. Two possible methods of extrapolating the outgoing characteristic variables are discussed. Finally, the numerical approach is validated for the 2D internal flow in a channel with a bump. [ABSTRACT FROM AUTHOR]

Euler equations are hyperbolic conservation law in compressible gas dynamics flow problem. In the non-linear problem, discontinuities or jump conditions may appear in the solutions. The numerical solutions typically produce oscillation near jump conditions because of truncation error. Weighted essentially non-oscillatory (WENO) scheme are adaptive high order method that suitable for the discontinuous function to minimize truncation error and diminish the oscillations. In this research, we use high order scheme to reduce numerical dissipation in hyperbolic conservation laws using WENO scheme that adopted as slope limiter in the finite volume coupled with Harten, Lax, van Leer-Contact (HLLC) flux to solve Euler equations. By some simple numerical tests in non-linear compressible flow problem, we found that the numerical results are non-oscillatory and very accurate. Numerical results show that the WENO scheme successfully implemented in finite volume methods to simulate non-linear compressible gas dynamics flow problem with satisfactory accuracy. [ABSTRACT FROM AUTHOR]

Modification of the serial Fortran code for solving unsteady 2D Euler equations for the mixture of compressible gas and polydisperse particles was carried out using OpenMP technology. Parallel code was used for the numerical simulation of shock wave propagation in 2D channel with obstacles filled with reactive Al-O2 gas particle mixture. Analysis was shown that obtained parallel speed-up is in a good agreement with the Amdahls law, which gives the estimate for serial code fraction about 30% [ABSTRACT FROM AUTHOR]

The results of comparative study of the WENO-type monotonization methods for numerical solution of the Euler equations computed by the discontinuous Galerkin method are presented. The variants of the technique based on Lagrangian and Hermitian interpolation are analyzed. Test simulations for the Sod problem, which solution contains a shock wave, a rarefaction wave, and a contact discontinuity, are performed. The merits and demerits of the considered variants of the limiters including the questions of the numerical solution monotonicity, numerical dissipation magnitude, computational costs and extensibility of software implementation are investigated. [ABSTRACT FROM AUTHOR]

Numerical modeling based on the Reynolds-averaged Navier - Stokes equations has shown qualitatively the possibility to realize controlled energy release and to obtain a transonic mode with the help of a transverse control air jet, as in modeling based on the Euler equations. The determining role in ignition in the vortex and detachment regions formed near the jets of hydrogen or ethylene and air are played by shock waves. [ABSTRACT FROM AUTHOR]

In this work we present the preliminary results of numerical simulations of detonation wave propagation in a plane channel conducted with an in-home code solving the chemically reacting Euler equations on supercomputers with GPUs. The simulations are performed with four detailed chemical kinetics mechanisms (ONERA, Deiterding, modified Jachimowski, Peterson and Hanson models). The latter model includes a pressure-dependent reaction. The 1D and 2D Euler equations are solved for a hydrogen/ oxygen mixture using high-order shock-capturing TVD schemes and a finite-rate chemistry solver. The sizes of detonation cells obtained with different models are compared. [ABSTRACT FROM AUTHOR]

A method of calculating the pressure from the velocity field measurement data by using the PIV contactless technique is considered in the work. The pressure distribution was calculated by using the momentum equation, which are given in the form of Euler equations for a two-dimensional stationary compressible gas flow with allowance for the continuity equation. The method of determining the pressure is applied for two characteristic streams: gradient (in pressure) and low-gradient. Flow visualization pictures obtained with the help of the schlieren method and the laser sheet technique are presented. The possibility of calculating the average pressure values from the velocity measurements by using the PIV method is shown. [ABSTRACT FROM AUTHOR]

A qualitative analysis of the collisional model of a two-phase medium is presented for the description of shockwave processes in dense gas particle mixtures. In the Euler equations, the chaotic motion of particles and their collisions are integrally taken into account. In general, the system has a composite type. Flow domains in which the system is hyperbolic are determined. The expansion of these domains with respect to the collisionless model is shown. Some numerical solutions of non-conservative equations of composite type with the use of monotonizing schemes of Harten and Gentry-Martin-Daly are obtained. The convergence properties of numerical solutions are established. Examples of shockwave structures with shocks in the particle phase are demonstrated. [ABSTRACT FROM AUTHOR]

The paper is devoted to the development of the numerical algorithm for the simulation of two-dimensional axisymmetric flows with shock waves in the domains with variable boundaries. Mathematical model is based on the Euler equations. The algorithm is verified on the problem about the motion of the single particle behind the transmitted shock wave. The simulation of the dynamics of two interacting particles behind the transmitted shock wave is carried out. [ABSTRACT FROM AUTHOR]

The paper is devoted to the numerical modeling of detonation initiation in the "multifocused" system - the flat channel with the profiled end-wall. Mathematical model is based on two-dimensional Euler equations supplemented by one-stage chemical kinetics model for the detonation of hydrogen-oxygen mixture under the low pressure. The specific feature of the numerical algorithm of the second approximation order is the usage of fully unstructured computational grids with the triangular cells. The mechanism of detonation initiation by the incident shock wave with the Mach number 2.58 in case of one elliptical reflector is described. [ABSTRACT FROM AUTHOR]

In the present work a computer code RCFS for numerical simulation of chemically reacting compressible flows on hybrid CPU/GPU supercomputers is developed. It solves 3D unsteady Euler equations for multispecies chemically reacting flows in general curvilinear coordinates using shock-capturing TVD schemes. Time advancement is carried out using the explicit Runge- Kutta TVD schemes. Program implementation uses CUDA application programming interface to perform GPU computations. Data between GPUs is distributed via domain decomposition technique. The developed code is verified on the number of test cases including supersonic flow over a cylinder. [ABSTRACT FROM AUTHOR]

The effect of a pulse-periodic energy deposition on the mixing of a supersonic jet interacting with an oblique shock wave is solved numerically using the two-dimensional (2D) Unsteady RANS (URANS) and Euler Equations (UEE). A low- or high-density air jet at Mj = 1.05 is injected into a cocurrent supersonic air stream with Mach number of M∞ = 2.5. The oblique shock is generated by a ramped step with a windward side inclination angle of 20 degree. The pulse-periodic energy supply realized above the jet, enhances the mixing significantly. Such effect is caused by the large-scale vortical structures generation due to baroclinic vorticity imposed in the shear layer and the suction effect of the vortex ring induced by the energy deposition zone interacting with oblique shock. A low 4.2% loss of the time averaged total pressure recovery coefficient is obtained at the outlet of the computational domain caused by energy deposition. The differences between predicted flow field structures in the framework of URANS and UEE are discussed. [ABSTRACT FROM AUTHOR]

The problem of the hydrodynamic interaction of turbomachine blade rows (cascades) is of great practical interest and is one of the most interesting problems from the point of view of the physical features of the resulting liquid or gas flow. Currently, it is extremely difficult to solve this problem by direct calculation of the three-dimensional Euler or Navier-Stokes equations. Therefore, efficient algorithms for successive calculations of exciting forces on blade cascades are developed using the model of ideal incompressible fluid flow past two relatively moving cascades which is uniform at infinity upstream of the cascades. This model is based on the assumption of low fluid velocity and the hypothesis of cylindrical cross-sections stating that the streamline surfaces are cylindrical surfaces, on each of which the flow is considered independently. [ABSTRACT FROM AUTHOR]

The slotted nozzles can be an alternative to Laval nozzles. The jets inflowing through the holes can be directed towards each other (opposing jets) or be focused at a single point on the axis (focused jets). It has been shown numerically and experimentally that it is necessary to consider the effect of viscosity for the numerical modeling of focused jets in order to predict the flow parameters on the channel surface. Nevertheless, the calculation accuracy based on the unsteady Euler equation is quite sufficient for averaged values in the output cross section. [ABSTRACT FROM AUTHOR]

The lid driven cavity problem has been studied numerically. The present work is focused on reviewing the fluid flow patterns for the lid driven cavity problem. The left, right and bottom walls are maintained at no slip boundary condition and the top wall is moved in the right direction with uniform velocity (u = 1.0). The governing equations are processed by the mass and momentum equations and solved by using the radial basis function (RBF) method. The governing equations are expressed using a primitive variable formulation. The method was based on implicit Euler scheme for temporal discretization and RBF method for spatial discretization. The effects of the Reynolds number on the fluid flow in the square cavity are investigated. Stream functions and pressure contours are presented for various Reynolds numbers, such as 102, 4x102 and 103. Comparing the numerical results obtained using the present method with other numerical methods from the literatures shows very good agreement. [ABSTRACT FROM AUTHOR]

Natural convection heat transfer within trapezoidal cavity has been studied numerically. The present study is attended to reviewed heat and fluid flow patterns for natural convection in a trapezoidal cavity with uniformly heated bottom wall. The left and right walls are maintained at uniform cold temperature and the top wall is assumed to be thermally insulated. The mathematical model is conducted by the mass, momentum and energy equations and solved by applying multiquadrics radial basis function (MQRBF) method. The MQRBF method is extended using an improved primitive variable formulation to solve the governing equations. The method was based on implicit Euler scheme for temporal discretization and MQRBF method for spatial discretization. The effects of Rayleigh number on the flow and heat transfer process in the trapezoidal cavity are investigated. Stream function, isothermal patterns and the Nusselt number are presented for the Rayleigh numbers varied as 10³, 104 and 105. Comparing the numerical results of a test case obtained using the present method with those obtained using finite element and finite volume method shows very good agreement. [ABSTRACT FROM AUTHOR]