In this paper we generate optimized Runge-Kutta stability polynomials for multidimensional discontinuous Galerkin methods recovered using the flux reconstruction approach. Results from linear stability analysis demonstrate that these stability polynomials can yield significantly larger time-step sizes for triangular, quadrilateral, hexahedral, prismatic, and tetrahedral elements with speedup factors of up to 1.97 relative to classical Runge-Kutta methods. Furthermore, performing optimization for multidimensional elements yields modest performance benefits for the triangular, prismatic, and tetrahedral elements. Results from linear advection demonstrate these schemes obtain their designed order of accuracy. Results from Direct Numerical Simulation (DNS) of a Taylor-Green vortex demonstrate the performance benefit of these schemes for unsteady turbulent flows, with negligible impact on accuracy.

在本文中，我们为使用通量重建方法恢复的多维不连续 Galerkin 方法生成优化的 Runge-Kutta 稳定性多项式。线性稳定性分析的结果表明，相对于经典的 Runge-Kutta 方法，这些稳定性多项式可以为三角形、四边形、六面体、棱柱形和四面体元素产生显着更大的时间步长，加速因子高达 1.97。此外，对多维单元执行优化可为三角形、棱柱和四面体单元带来适度的性能优势。线性平流的结果表明这些方案获得了它们设计的精度顺序。