Efficiency benchmarking of seventh-order tri-diagonal weighted compact nonlinear scheme on curvilinear mesh

Abstract

ABSTRACTEfficiency improvements of high-order weighted compact nonlinear scheme (WCNS) are verified using a series of benchmark cases, proposed at the International Workshop on High-Order CFD Methods. A seventh-order tri-diagonal compact one of WCNSs (WCNS-E8T7), constructed in recent years, is investigated as a basic scheme, and compared to a typical fifth-order explicit WCNS (WCNS-E6E5) and a traditional second-order TVD scheme MUSCL. Among these tests, a symmetrical conservative metric method (SCMM) is adopted to ensure the accuracy and robustness of WCNSs when solving cases in the curvilinear coordinates. The computational efficiency of schemes is evaluated based on a non-dimensional cost in achieving the same level of accuracy. Related results show that WCNS-E8T7 has a better performance than WCNS-E6E5 with the same interpolation stencils. Moreover, the opinion that high-order methods can obtain higher computational efficiency than second-order methods is demonstrated on the cases ranging from academic problems to real-life computations.