DG方法求解可压缩气固两相流动

给出求解双向耦合可压缩气固两相流的间断有限元方法，对所得到的气固两相流方程组不需要采用分裂的方法离散，对气相、颗粒相方程及其对流部分和源项可以统一处理，两相都采用基于近似Riemann解的数值通量.数值模拟低压含尘激波管内的两相非平衡流动，并与平衡流、冻结流的结果进行比较.分析颗粒相的存在对气体运动的影响，及激波后松弛区域内两相间相互作用规律.发现颗粒质量比决定两相平衡后的最终状态，而颗粒直径决定两相流从非平衡到平衡的过渡过程，即不同尺寸颗粒对应的驰豫时间、松弛距离不同.结果表明：本文提出的计算方法对求解可压缩气固两相流是可行的，为研究复杂的气固两相流动问题奠定了基础.

DG Method for Compressible Gas-Solid Two-phase Flow

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.