论文标题
通过考虑不同的特征值解决方案，对两层浅水系统的一阶数值方案的重新评估效率
Re-evaluating efficiency of first-order numerical schemes for two-layer shallow water systems by considering different eigenvalue solutions
论文作者
论文摘要
本文通过考虑不同的特征值溶液评估了两层浅水方程的几种一阶数值方程的效率。具体而言，在ROE，中间场捕获（IFCP）和多项式粘度矩阵（PVM）方案中实现时，分析了数值，分析和近似特征值求解器的精度和计算成本。在计算两层浅水流时，进行了几项数值测试以检查具有不同特征值求解器的数值方案的总体效率。结果表明，分析解决方案比数值求解器要快得多，其计算成本更接近近似表达式。因此，具有分析解决方案的ROE方案要快得多，总体效率等于IFCP方案。另一方面，发现具有分析溶液对特征值的IFCP和PVM方案与具有近似表达式的IGENVALES同样有效。分析特征值在处理层之间的密度差时显示出更好的结果。
The efficiency of several first-order numerical schemes for two-layer shallow water equations are evaluated in this paper by considering different eigenvalue solutions. Specifically, the accuracy and computational cost of numerical, analytical, and approximated eigenvalue solvers are analysed when implemented in Roe, Intermediate Field CaPturing (IFCP) and Polynomial Viscosity Matrix (PVM) schemes. Several numerical tests are performed to examine the overall efficiency of numerical schemes with different eigenvalue solvers when computing two-layer shallow-water flows. The results show that analytical solutions are much faster than numerical solvers, with a computational cost closer to approximate expressions. Consequently, Roe schemes with analytical solutions to the eigenstructure are much faster, with overall efficiency equal to IFCP scheme. On the other hand, IFCP and PVM schemes with analytical solutions to eigenvalues are found to be equally efficient as those with approximated expressions. Analytical eigenvalues show slightly better results when dealing with a larger density difference between the layers.
