Peculiarities of a numerical solution of the problem of shock wave propagation over a gas suspension with small particles

Based on the interpenetrating continua approach, the numerical solution of the problem of shock wave propagation in a gas suspension containing inert particles of negligible volume fraction is studied. The solution of the governing equations was obtained numerically using the finite volume method with the difference scheme of the first order of accuracy in time and space. The flux values on the faces of the difference cells for the gas are found by van Leer’s method; for the particles, by Kraiko's method. The implicit and explicit implementations for the right-hand side of the governing equations taking into account the interaction of gas and particles are considered in the difference scheme. The dependence of the maximum possible size of the difference grid on the diameter of the particles is obtained to achieve a stable solution using the explicit difference scheme. It is shown that the implicit difference scheme applied for the righthand sides of equations makes it possible to obtain a stable solution on the fixed difference grid in a wide range of particle sizes. The relaxation processes are shown to significantly affect the shock wave structure and the contact discontinuity propagating along the gas suspension with large particles. The dependence of the shock wave width on the particle size is obtained, which is in a good agreement with the analytical estimates.