Extension of the self-similar structures based genuinely two-dimension Riemann solver called MuSIC (Multidimensional, Self-similar, strongly-Interacting, Consistent) to curvilinear coordinate systems are conducted in this study. Built upon Balsara's work, the MuSIC1 (MuSIC considering the 1st order moment) scheme solves the compressible Euler equations in curvilinear coordinates by considering the first moment in the similarity variables, and the MuSIC2 (MuSIC considering the 2nd order moment) scheme considers the second moment in the similarity variables. Systematic numerical test cases are conducted. One dimensional cases indicate that both MuSIC1 and MuSIC2 are capable of accurately capturing one-dimensional shocks and expansion waves. Also, MuSIC2 is with a higher resolution than MuSIC1 in capturing linear contact discontinuities because it considers the linear variation of similarity variables in strongly-interacting zones. Two dimensional isotropic case shows that the self-similar structures based genuinely two-dimensional Riemann solvers can help improve the traditional one-dimensional Riemann solvers' mesh imprinting phenomenon remarkably. The other two-dimensional cases show that MuSIC2 is with a high resolution in simulating multidimensional complex flows in both Carestein coordinates and curvilinear coordinates, while MuSIC1 performs worse due to its lack of accuracy in resolving linear variation of similarity variables in resolved states.

在这项研究中，将基于真正的二维Riemann解算器MuSIC（多维，自相似，强相互作用，一致）的自相似结构扩展到曲线坐标系。在Balsara的工作基础上，MuSIC1（考虑一阶矩的MuSIC）方案通过考虑相似变量中的第一矩来求解曲线坐标中的可压缩Euler方程，而MuSIC2（考虑二阶矩的MuSIC）方案则考虑了第二矩在相似性变量中。进行了系统的数值测试案例。一维情况表明MuSIC1和MuSIC2都能够准确捕获一维冲击和扩展波。也，MuSIC2在捕获线性接触不连续性方面比MuSIC1具有更高的分辨率，因为它考虑了强交互区域中相似性变量的线性变化。二维各向同性情况表明，基于真正的二维Riemann求解器的自相似结构可以显着改善传统的一维Riemann求解器的网格印迹现象。其他二维情况表明，MuSIC1在模拟Carestein坐标和曲线坐标中的多维复杂流方面具有较高的分辨率，而MuSIC1的性能较差，这是因为MuSIC1在解析状态下相似变量的线性变化方面缺乏准确性。二维各向同性情况表明，基于真正的二维Riemann求解器的自相似结构可以显着改善传统的一维Riemann求解器的网格印迹现象。其他二维情况表明，MuSIC2在模拟Carestein坐标和曲线坐标中的多维复杂流方面具有较高的分辨率，而MuSIC1在解析状态下相似变量的线性变化方面缺乏准确性，因此表现较差。二维各向同性情况表明，基于真正的二维Riemann求解器的自相似结构可以显着改善传统的一维Riemann求解器的网格印迹现象。其他二维情况表明，MuSIC1在模拟Carestein坐标和曲线坐标中的多维复杂流方面具有较高的分辨率，而MuSIC1的性能较差，这是因为MuSIC1在解析状态下相似变量的线性变化方面缺乏准确性。