Distinctive features of calculating interaction between shock wave and gas bubble in a finely dispersed gas suspension

The problem of interaction between shock wave and gas bubble in a finely dispersed gas suspension is studied using a two-velocity two-temperature formulation. The numerical method, which is applicable for a simulation of multiphase flows governed by the stiff Euler equations, is utilized. Implementation of the scheme is split into two phases. The first uses the central differences of both deformation and gradient terms with Christensen-type artificial viscosity. The total variation diminishing (TVD)-type reconstructions of the fluxes are used in the second phase applying a weighted linear combination of upwind and central approximations of convective terms with flux limiters. The second-order TVD Runge–Kutta (RK) algorithm is employed to march the solution in time. A high stability is ensured by either implicit or semi-implicit calculating method for the source terms in the equations, which have been proposed and developed over the last decades. The properties of elaborated numerical method are verified by considering several challenging one- and two-dimensional test problems as compared to the exact self-similar equilibrium solutions and to the results of other authors. A convergence to the equilibrium solutions is confirmed at various particle sizes. The shock-wave pattern, the Richtmyer–Meshkov instability developing along the bubble interface, and the large-scale turbulence generation are studied.