This paper extends the high-order entropy stable (ES) adaptive moving mesh finite difference schemes developed in Duan and Tang (2022) to the two- and three-dimensional (multi-component) compressible Euler equations with the stiffened equation of state (EOS). The two-point entropy conservative (EC) flux is first constructed in the curvilinear coordinates, which is nontrivial in the case of the stiffened EOS. With the aid of the high-order discretization of the geometric conservation laws and the linear combinations of the two-point EC fluxes, the high-order semi-discrete EC schemes are derived. The high-order semi-discrete ES schemes are constructed by adding suitable high-order dissipation term to the EC schemes such that the semi-discrete entropy inequality is satisfied and unphysical oscillations are suppressed. The high-order dissipation term is built on the multi-resolution weighted essentially non-oscillatory (WENO) reconstruction and the newly derived scaled eigenvector matrices. 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 appropriate monitor function, which is adapted to the multi-component flow and encodes more physical characteristics of the solutions. 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 effectively capture the localized structures of the proposed schemes.

本文将 Duan 和 Tang (2022) 开发的高阶熵稳定 (ES) 自适应移动网格有限差分方案扩展到具有硬化状态方程 (EOS ) 的二维和三维（多分量）可压缩欧拉方程）。两点熵保守 (EC) 通量首先在曲线坐标中构建，这在硬化 EOS 的情况下是不平凡的。借助几何守恒定律的高阶离散化和两点EC通量的线性组合，推导出高阶半离散EC格式。高阶半离散 ES 方案是通过在 EC 方案中添加合适的高阶耗散项来构造的，使得半离散熵不等式得到满足并且非物理振荡被抑制。高阶耗散项建立在多分辨率加权基本非振荡 (WENO) 重建和新导出的缩放特征向量矩阵的基础上。时间离散化采用显式保稳Runge-Kutta方法，通过迭代求解网格重分布方程和适当的监控函数，自适应重分布网格点，适应多分量流，编码更多物理解决方案的特点。使用 MPI 编程在并行计算机系统上进行了几个 2D 和 3D 数值测试，以验证准确性和有效捕获所提出方案的局部结构的能力。