This paper extends the high-order entropy stable (ES) adaptive moving mesh finite difference schemes developed in [14] to the two- and three-dimensional (multi-component) compressible Euler equations with the stiffened equation of state. The two-point entropy conservative (EC) flux is first constructed in the curvilinear coordinates. The high-order semi-discrete EC schemes are given with the aid of the two-point EC flux and the high-order discretization of the geometric conservation laws, and then the high-order semi-discrete ES schemes satisfying the entropy inequality are derived by adding the high-order dissipation term based on the multi-resolution weighted essentially non-oscillatory (WENO) reconstruction for the scaled entropy variables to the EC schemes. The explicit strong-stability-preserving Runge-Kutta methods are used for the time discretization and the mesh points are adaptively redistributed by iteratively solving the mesh redistribution equations with an appropriately chosen monitor function. Several 2D and 3D numerical tests are conducted on the parallel computer system with the MPI programming to validate the accuracy and the ability to capture effectively the localized structures of the proposed schemes.
翻译:本文扩展了在[14] 中制定的高顺序适应性活性移动网状差异(ES)稳定网状(ES)适应性移动网状差异方案,将其延伸至以硬度方程式为基础的二维和三维(多构件)压缩 Euler 等式。两点偏偏保守(EC)通量首先建在曲线线坐标处。高序半分异EC方案在两点EC通量和几何保护法高度分解的帮助下实施,然后通过添加基于多分辨率加权基本上非悬浮(WENO)的多分级分级分级分解(高分解)埃利(ES)等式高序分级半分解(ES)计划,通过添加基于多分制加权基本上非悬浮的(WENO)等式等式高序分解(EU)等式(EU)等式等式。高序半分解(ERS)通量半分解(E)通量半分解(E)通通通量半分流(E-E-EC-EC-E-EC-EC-EC-EC-EC-EC-EC-EC-EC-EC-EC-EC-EC-EC-EC-EC-EC-ES-ES-E-E-E-E-E-E)方案)方案,然后通过迭接合调和高序分解(E-E-ES-ES-ES-E-E-E-E-ES-E-S-S-S-E-E-E-E-E-E-E-E-E-C-C-C-C-C-C-C-C-C-C-C-C-C-C-C-C-C-C-C-C-C-C-C-C-C-C-C-C-C-C-C-C-C-C-C-C-C-C-C-C-C-C-C-C-C-C-C-C-C-C-C-C-C-C-C-C-C-C-C-C-C-C-C-C-C-C-C-C-C-C-C-C-C-C-C-C-C-C-