2024 Volume 32 Pages 369-379
Cascadic Parareal is a parallel-in-time (PinT) method developed to improve the parallel performance for explicit time-dependent problems. It is more efficient than other PinT methods when explicit methods are used for solving. Cascadic Parareal has been proven to accelerate a one-dimensional advection problem and a two-dimensional compressible flow simulation faster compared to spatial parallelism with more than 64 cores in the previous works. However, Cascadic Parareal has also demonstrated slow convergence and produced unstable results for supersonic flow simulations. The instability is caused by unstable supersonic flow results calculated on the coarse meshes. In the present work, we introduce an improvement for Cascadic Parareal using local mesh refinement (LMR) to improve its accuracy for supersonic flow simulations. Numerical experiments in this research demonstrate that the LMR method can improve the convergence rate and accuracy of Cascadic Parareal for supersonic flow simulations. The numerical experiments of the present work show that the improved PinT method can provide stable and more accurate simulations for supersonic flow, and the compute time performance of the PinT algorithm can outperform simple spatial parallelism.
