Abstract Explicit two-step Runge-Kutta (TSRK) methods offer an efficient alternative to traditional explicit Low-Storage Runge-Kutta (LSRK) schemes for solving the Navier-Stokes equations. A special class of TSRK methods that reduce requirement compared to previous TSRK schemes are derived. Schemes of fourth, fifth and sixth order are implemented and tested. The new schemes are evaluated with two common test cases, a 2D cylinder and a 3D Taylor-Green vortex. The results are compared with classical time discretization strategies. Timings obtained in three different hardware configurations show that the new TSRK methods of order four are 25% faster than LSRK schemes of the same order. Fifth and sixth order TSRK methods are tested with the same 3D test case and the results are compared to LSRK algorithms. Results show TSRK schemes of fifth and sixth order are competitive compared to LSRK methods of the same orders, as LSRK methods are of second order for non linear differential systems.

中文翻译：

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用于流体动力学模拟的高效两步 Runge-Kutta 方法

摘要 显式两步 Runge-Kutta (TSRK) 方法为求解 Navier-Stokes 方程提供了传统显式低存储 Runge-Kutta (LSRK) 方案的有效替代方案。派生出一类特殊的 TSRK 方法，与以前的 TSRK 方案相比，它减少了要求。实现并测试了四阶、五阶和六阶方案。新方案通过两个常见的测试案例进行评估，一个 2D 圆柱体和一个 3D Taylor-Green 涡流。结果与经典的时间离散化策略进行了比较。在三种不同硬件配置中获得的时序表明，新的四阶 TSRK 方法比相同阶的 LSRK 方案快 25%。五阶和六阶 TSRK 方法使用相同的 3D 测试用例进行测试，并将结果与​​ LSRK 算法进行比较。