Optimal Runge-Kutta Stability Polynomials for Multidimensional High-Order Methods
| Autor: | Siavash Hedayati Nasab, Carlos A. Pereira, Brian C. Vermeire |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Numerical Analysis
Quadrilateral Speedup Applied Mathematics General Engineering Direct numerical simulation Order of accuracy 01 natural sciences Stability (probability) Mathematics::Numerical Analysis 010305 fluids & plasmas Theoretical Computer Science 010101 applied mathematics Computational Mathematics Runge–Kutta methods Computational Theory and Mathematics Discontinuous Galerkin method 0103 physical sciences Tetrahedron Applied mathematics 0101 mathematics Software Mathematics |
| Zdroj: | Journal of Scientific Computing. 89 |
| ISSN: | 1573-7691 0885-7474 |
| DOI: | 10.1007/s10915-021-01620-x |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full text from SpringerLink