| Abstract |
In this study, we present strategies to improve the computational efficiency of high-order space-time DG. The relation between DG in time and implicit Runge-Kutta methods is discussed further and efficient smoothing strategies for solving the implicit systems at each time step are investigated. We suggest a simple IMEX multi-stage optimized RK scheme for pseudo-time stepping that treats the spatial residual explicitly and the temporal residual implicitly. An IMEX four-stage optimized RK scheme has been tested for the isentropic vortex problem at high spatial and temporal orders. For small physical time steps, the IMEX scheme provides an 8.7x speedup over the purely explicit pseudo-time stepping scheme. For large physical time steps, the IMEX scheme reduces to an explicit RK scheme optimized for stability in pseudo-time and provides 7.8x faster convergence rate than single-stage RK scheme in pseudo-time. The performance of the IMEX pseudo-time stepping scheme is examined for flow over a NACA0012 airfoil in 2D and 3D as a function of the physical time step size and variations in grid resolution, showing superior performance to the equivalent explicit RK scheme using either local or global minimum time stepping in pseudo time. |
| Authors |
Sung-Hwan Yoon  , Andrew Kirby  , Dimitri J. Mavriplis
|
| Journal Info |
Not listed | AIAA SCITECH 2023 Forum
|
| Publication Date |
1/19/2023 |
| ISSN |
Not listed |
Type |
article |
| Open Access |
closed
|
| DOI |
https://doi.org/10.2514/6.2023-0662 |
| Keywords |
Discontinuous Galerkin Methods (Score: 0.541938) , Stabilized Methods (Score: 0.502973)
|
