We present DG method for solving two-way coupling compressible gas-solid two-phase flow. Equations of both phases are discreted simultaneously, including convection term and source term. Splitting technique to discretize governing equations separately is avoided. Numerical flux of both phases is based on approximate Riemann solver. Dusty-gas shock tube problem with particles in low pressure section is simulated. Comparisons of equilibrium flow and frozen flow are made. Influence of particles in gas and interaction rules between two phases in relaxation zone behind shock are studied. It found that mass ratio of particles determines last equilibrium state and particles diameter determines transition process of two-phase flow from nonequilibrium to equilibrium flow. Namely, different diameter particles correspond to different relaxation time and distance. It shows that the numerical method proposed is reliable. It lays a foundation for more complicated gas-solid two-phase flow problems.

A study on oblique shock wave reflection in condensed matter is carried out by means of numerical simulation and theoretical analysis.Runge-Kutta control volume discontinuous finite element method is used to solve Euler equations.Equations of state for condensed matter adopt "stiffen gas" formulas.Patterns of oblique shock wave reflection in condensed matter are discussed.A shock polar theory is employed in analyzing critical agles of transition from regular reflection to irregular reflection.It gives states of reflected shock wave.Numerical results and shock polar solutions are compared and typical oblique shock wave reflections are obtained.

Runge-Kutta control volume discontinuous finite element method (RKCVDFEM) is proposed to solve numerically hyperbolic conservation laws,in which space discretization is based on control volume finite element method (CVFEM) while time discretization is based on a second order accurate TVB Runge-Kutta technique.Piecewise linear function space is chosen as finite element space.The scheme is total variation bounded (TVB) and is formally second order accurate in space and time.Numerical examples show that numerical solution converges to the entropy solution,and order of convergence is optimal for smooth solution.Compared with numerical results of Runge-Kutta discontinuous Galerkin method (RKDGM) those of RKCVDFEM are better.

The block-up coefficient technique and the finite volume approach are used to solve numerically the complete N-S equations in a square enclosure with spacers. A pressure-velocity correction algorithm (SIMPLE-C, Semi-Implicit Method for Pressure Linked Equation-Consistent) is adopted in the direct calculation of all the physical variables. The applicability, feasibility and efficiency of the block-up coefficient technique applied to simulate three-dimensional viscous flows are investigated.The primary results have shown that the block-up coefficient technique is indeed a simple and convenient numerical approach, with encouraging prospects, for computing the velocity, pressure and other physical quantities for the flows in a channel with complex boundary shape.