This paper presents three Riemann solvers for the Wilkins model of hypoelasticity with the Jaumann derivative correction. The solvers are developed as extensions of the HLL and HLLC Riemann solvers for the Euler hydrodynamic model and differ in the number of waves considered (two-wave HLLEPJ Riemann solver, three-wave HLLCEPJ Riemann solver and five-wave HLLCEPJ Riemann solver). The discontinuous solution of the Wilkins system of equations is obtained using generalized Rankine-Hugoniot relations developed on the basis of the path-conservative DLM approach. A special choice of the path in the phase space allows to avoid any iterative processes in the solver construction. The proposed Riemann solvers are implicated in the first order Finite Volume numerical scheme for testing on the set of 1D, 2D and 3D problems of elastoplastic flows.

The Wilkins model for an elastoplastic medium is considered. A theoretical analysis of discontinuous solutions under the assumption of one-dimensional uniaxial strain is performed. In this approximation, the material equations for the deviator stress tensor components are integrated exactly, and only the conservative part of the governing equations remains, which makes it possible to derive a class of exact analytical solutions for the model. To solve the full nonconservative system of equations (without assuming the uniaxial strain), a Godunov-type numerical method is developed, which uses an approximate Riemann solver based on integrating the system of equations along a path in the phase space. A special choice of path is proposed that reduces the two-wave HLL approximation to the solution of a linear equations. Numerical and exact analytical solutions are compared for a number of problems with various regimes of shockwave processes.

Compressible multiphase flows with resolved interfaces are numerically simulated. The Baer–Nunziato relaxation model, which is nonequilibrium with respect to velocity, pressure, and temperature, is used. The basic elements of the proposed approach are a simple model for local sub-cell reconstruction of the interface near a cell face and the simulation of relaxation processes in mixed cells by solving the composite Riemann problem. Two approximate solutions of this problem are proposed that take into account the interaction of primary waves and the formation of secondary waves based on HLL- and HLLC-type Riemann solvers. The method does not require any special relaxation parameters and supports, in fact, a diffusion-free interface resolution, which is demonstrated by numerically solving test problems.

The paper addresses a new method for approximately solving the Riemann problem for an arbitrary non-conservative hyperbolic system of partial differential equations. The method is based on the reconstruction of the complete wave structure in the Riemann problem with using the Borel measures interpretation (path-representation) of the non-conservative products. In contrast to alternative approximate methods of the Riemann problem solution, e.g., HLL-type methods, the method proposed takes into account the complete wave structure of the solution and requires the calculation of only eigenvalues and eigenvectors of the matrix of the system to be considered and therefore can be easy realized for any hyperbolic system. In the case of conservative systems, the method gives the exact Riemann problem solution with any required accuracy. It can be applied, for example, to compute the exact Rieman problem solution for compressible Euler equations with an arbitrary equation of state. The method is applied to solving the Rieman problem for the Euler equations, the two-phase Baer-Nunziato equations, the elasto-plastic equations. The results obtained concern the convergence and accuracy propreties of the method. (C) 2020 Elsevier Ltd. All rights reserved.

The results of research on the effect of the presence of viscosity on evolution of perturbations in the system of colliding plates are presented in this work. The range of amplitudes of the initial perturbations wavelengths, at which the effect of viscosity may be neglected, are determined. Comparison of analytical and numerical results are shown.

The problem of two semi-infinite plates under impact is studied both theoretically and numerically. Initially, one plate has the perturbed density field with uniform distribution of pressure. We demonstrate that various regimes of instabilities development in plates are guided by the appropriate initial conditions. A viscosity effect on instabilities growth is analyzed. Particularly, the minimal wavelength of an initial perturbation, for which viscosity effect is negligible, is obtained. The performed numerical simulations support our theoretical insights.

We consider modelling gas-solid granular mixture flow in a wide range of solid volume fractions. In such flows, concentration of the solid phase changes from dilute (low concentration) to dense (high concentration). Several macroscopic phenomenological models have been developed for gas-solid granular medium. The 6-wave 7-equation Baer-Nunziato model (BN) has been designed for gas-solid granular mixtures with dense concentration of the solid phase. Dilute mixtures are commonly modeled with the one-pressure model that is not hyperbolic in the whole range of model parameters. In the paper we are concerned with the problem of combaining the two models. We develop a new model of two-phase compressible flows which is hyperbolic and thermodynamically consistent and covers a wide range of solid phase concentrations in an unique approach. We tets the proposed model on several problems where the flow regime is changed from dilute to highly packed mixtures. The numerical calculations are carried out with moving adaptive Eulerian grids. The Godunov method is used with approximation of the non-conservative numerical flux with the HLLEM method.

The paper considers flow modeling of two-phase heterogeneous medium. Each phase of the medium is considered as continuum, which is described by the compressible Euler equations. The phases are separated by the contact surface (interface) and are not mixed on the molecular level. Examples of such medium are: mixtures of solid particles and gas (in dense or dilute concentration of particles), liquids with small bubbles, solid porous materials filled with gas or liquid. The phase can be of connected structure (dense particles, porous solid, gas between dilute particles, etc.) or of non-connected structure (separated inclusions as gas bubbles, dilute particles, closed pores in solid, etc.). The connectivity of the phase is closely related to the propagation of acoustic perturbations. An attempt was made to consider all the cases of the phase connectivity in the framework of a unique approach. The paper presents an approach that couples the models designed for different cases of phase connectivity to the generalized hyperbolic and thermodynamically consistent form. The proposed model is applicable for simulating flows with change of the phase connectivity, e.g. dense-to-dilute two-phase flows. The model is verified on several problems of gas–solid granular medium flows. In numerical simulations the Godunov method with the HLLEM flux approximation on arbitrary moving Euler grids is used.

The paper addresses a numerical approach for solving the Baer-Nunziato equations describing compressible 2-phase flows. We are developing a finite-volume method where the numerical flux is approximated with the Godunov scheme based on the Riemann problem solution. The analytical solution to this problem is discussed, and approximate solvers are considered. The obtained theoretical results are applied to develop the discrete model that can be treated as an extension of the Rusanov numerical scheme to the Baer-Nunziato equations. Numerical results are presented that concern the method verification and also application to the deflagration-to-detonation transition (DDT) in porous reactive materials.

In this work we consider the problem of high-velocity impact of a solid impactor on the layer of spherical solid particles. The impact initiates a wave-type process of compaction of particles in the layer, and the ejection of small solid particles from the compacted layer surface to the air. The first part of the paper addresses modelling the process of particle compaction and the initial stage of solid ejection with the SPH method. In the second part presented below, we consider the process of compaction and solid mass ejection using a new non-equilibrium two-phase model of the granular medium. This model makes it possible to describe mechanics of two-phase gas-solid medium in a wide range of the phase volume fraction, from regimes of isolated particle flows to regimes of dense packed particles.

According to the data obtained by the Photonic Doppler Velocimetry (PDV) shock wave propagation through a layer of bulked metallic particles produces dust ejecta consisting of fragments with various velocities. While velocity distribution of dust particles can be measured by the PDV, the spatial mass distribution and size distribution of the fragments are hard to derive from the PDV experimental data. To study the mechanism of ejecting and composition of ejected material, direct simulation of experimental conditions is performed with the massive-parallel SPH code. We find that the cumulative jets are produced by the collisions of neighbor spheres accelerated by a shock wave. Those of jets which are able to reach free boundary, leave the layer and decay with formation of many fragments. The data we acquire via direct numerical simulation of the described process is used as initial data for further investigation of dust motion in the air with the finite differences method.

The distinctive features of the process involving the collision of a elastoplastic cylinder with a non-deformable wall are investigated numerically: the dependence of the dynamics of the interaction on the coefficient of friction between the impactor and the obstacle, the dependence of the final shape of the impactor and the duration of its contact with the obstacle on the initial velocity and length of the cylinder, the distinctive features of the dynamics of the change in the contact area of the impactor and obstacle and of the velocities of motion of the contact discontinuity points, etc. The calculations are carried out in an axisymmetric formulation using the “TIS” original software package in which the method of splitting with respect to physical processes and the finite volume method for moving Euler meshes are implemented.

The present paper is concerned with a numerical model that is developing to simulate dynamical processes in a heterogeneous two-phase medium consisting of two components-elastic-plastic porous solid and gas that occupies the domain in between of the solid. The scope of our interest is regimes of large deformations and intense loading-unloading processes when the solid and the gas have different velocities and temperatures, i.e., are in dynamical and thermal non-equilibrium. Such a model needs to describe, for example, combustion and detonation in condensed porous explosives that are manufactured by pressing granular propellants.