Two-dimensional Riemann solver for Euler equations of gas dynamics
Two-dimensional Riemann solver for Euler equations of gas dynamics
复制标题
DOI：
10.1006/jcph.2000.6666
复制
发表时间：
2001-02
影响因子：
4.1
通讯作者：
M. Brio;A. Zakharian;G. Webb
中科院分区：
文献类型：
--
作者：
M. Brio;A. Zakharian;G. Webb
基于Roe （1981， J. Comput）对一维方法的推广，我们构建了一个基于二维线性波对数值通量贡献的Riemann求解器。物理学报，43,157)。该求解器基于多态黎曼问题，适用于任意三角形网格或平面的任何其他有限体积镶嵌。我们给出了用一阶和二阶精确数值解来说明该方法的性能的数值例子。数值通量的贡献是由于源自计算单元角落的一维波和多维波。在适当的CFL限制下，一维波的贡献在通量中占主导地位，这解释了维数分裂解在实践中具有良好的性能。多维通量修正增加了精度和稳定性，允许更大的时间步长。改进在粗网格和大CFL数上更为明显。对于二阶方法，改进可以与较少扩散限制器所产生的改进相媲美。
Abstract We construct a Riemann solver based on two-dimensional linear wave contributions to the numerical flux that generalizes the one-dimensional method due to Roe (1981, J. Comput. Phys. 43 , 157). The solver is based on a multistate Riemann problem and is suitable for arbitrary triangular grids or any other finite volume tessellations of the plane. We present numerical examples illustrating the performance of the method using both first- and second-order-accurate numerical solutions. The numerical flux contributions are due to one-dimensional waves and multidimensional waves originating from the corners of the computational cell. Under appropriate CFL restrictions, the contributions of one-dimensional waves dominate the flux, which explains good performance of dimensionally split solvers in practice. The multidimensional flux corrections increase the accuracy and stability, allowing a larger time step. The improvements are more pronounced on a coarse mesh and for large CFL numbers. For the second-order method, the improvements can be comparable to the improvements resulting from a less diffusive limiter.