This paper develops the high-order entropy stable (ES) finite difference schemes for multi-dimensional compressible Euler equations with the van der Waals equation of state (EOS) on adaptive moving meshes. Semi-discrete schemes are first nontrivially constructed built on the newly derived high-order entropy conservative (EC) fluxes in curvilinear coordinates and scaled eigenvector matrices as well as the multi-resolution WENO reconstruction, and then the fully-discrete schemes are given by using the high-order explicit strong-stability-preserving Runge-Kutta time discretizations.The high-order EC fluxes in curvilinear coordinates are derived by using the discrete geometric conservation laws and the linear combination of the two-point symmetric EC fluxes, while the two-point EC fluxes are delicately selected by using their sufficient condition, the thermodynamic entropy and the technically selected parameter vector.The adaptive moving meshes are iteratively generated by solving the mesh redistribution equations, in which the fundamental derivative related to the occurrence of non-classical waves is involved to produce high-quality mesh. Several numerical tests on the parallel computer system with the MPI programming are conducted to validate the accuracy, the ability to capture the classical and non-classical waves, and the high efficiency of our schemes in comparison with their counterparts on the uniform mesh.

翻译：本文针对自适应移动网格上具有van der Waals状态方程的多维可压缩Euler方程，发展了高阶熵稳定有限差分格式。首先基于新推导的曲线坐标系高阶熵守恒通量、缩放特征向量矩阵以及多分辨率WENO重构，非平凡地构造了半离散格式；随后采用高阶显式强稳定保持Runge-Kutta时间离散方法给出全离散格式。曲线坐标系高阶熵守恒通量的推导运用了离散几何守恒律与两点对称熵守恒通量的线性组合，而两点熵守恒通量则通过其充分条件、热力学熵及技术性选取的参数向量进行精细构造。自适应移动网格通过迭代求解网格重分布方程生成，其中引入与非经典波出现相关的基本导数以产生高质量网格。在采用MPI编程的并行计算机系统上进行了多项数值试验，验证了格式的精度、捕捉经典与非经典波的能力，以及与均匀网格对应格式相比的高效性。