可压缩流体流动的单侧GRP求解器和数值边界条件
One-sided GRP Solver and Numerical Boundary Conditions for compressible fluid flows
摘要：
在可压缩流体流动的计算中，数值边界条件通常是计算边界上所有物理量都必须满足的，而物理边界条件通常是部分物理量。传统上通常采用某些外推技术或鬼单元来解决这个问题，但通常会出现虚假波反射，从而导致数值不稳定性。在本文中，我们将这个问题与单侧广义黎曼问题（GRP）求解器的加速活塞问题的气体动力学，使外推技术实际上可以避免。实际上，相容性论证自然要求将单侧广义黎曼问题公式化，并将其纳入边界条件的数值处理中。至于非线性波与物理边界的相互作用，这样的单边GRP求解器显示出显着的效果，数值实验表明，在避免虚假波反射的计算边界。
英文摘要：
In the computation of compressible fluid flows, numerical boundary conditions are always necessary for all physical variables at computational boundaries while just partial physical variables are often prescribed as physical boundary conditions. Certain extrapolation technique or ghost cells are often employed traditionally for this issue but spurious wave reflections often arise to cause numerical instability. In this paper, we associate this issue with the one-sided generalized Riemann problem (GRP) solver motivated by the accelerated piston problem in gas dynamics so that the extrapolation technique can be actually avoided. In fact, the compatibility arguments naturally requires to formulate the one-sided generalized Riemann problem and incorporate it into the numerical procedure of boundary conditions. As far as the interaction of nonlinear waves with physical boundaries, such a one-sided GRP solver shows significant effects, as numerical experiments demonstrate, on avoiding spurious wave reflections at the computational boundaries.
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