Two-level dynamic load-balanced p-adaptive discontinuous Galerkin methods for compressible CFD simulations

We present a novel approach utilizing two-level dynamic load balancing for p-adaptive discontinuous Galerkin (DG) methods in compressible Computational Fluid Dynamics (CFD) simulations. The high-order explicit first stage, specifically the singly diagonal implicit Runge–Kutta (ESDIRK) method, is employed for time integration, where the pseudo-transient continuation is integrated with the restarted generalized minimal residual (GMRES) method to handle the solution of nonlinear equations at each stage of ESDIRK, excluding the initial stage. Relying on smoothness indicators, we carry out the refinement/coarsening process for p-adaptation with dynamic load balancing. This approach involves a coarse level (distributed memory) decomposition based on MPI paradigm and a fine level (shared memory) decomposition based on OpenMP paradigm, enhancing parallel efficiency. Dynamic load balancing is achieved by computing weights based on degrees of freedom, ensuring balanced computational loads across processors. The parallel computing framework adopts either a graph-based type (ParMETIS and Zoltan) or space-filling curves type (GeMPa) for coarse level partitioning, and a graph-based type (METIS and Zoltan) for fine level partitioning. The effectiveness of the method is demonstrated through numerical examples, highlighting its potential to significantly improve the scalability and efficiency of compressible flow simulations. The numerical simulations were conducted using the CODA flow solver, a state-of-the-art tool developed collaboratively by the French National Aerospace Center (ONERA), the German Aerospace Center (DLR), and Airbus.