A hybrid parallel algorithm for solving euler equation using explicit RKDG method based on OpenFOAM

OpenFOAM is a framework of the open source C++ CFD toolbox for flexible engineering simulation, which uses finite volume method (FVM) in the discretization of partial differential equations (PDEs). The problem solving procedure in OpenFOAM consists in equations dicretization stage, equations solving stage and field limiting stage. The best parallelism is limited by the equation solving stage, which contains communications. Compared to FVM, discontinuous Galerkin (DG) method is a high-order discretization method, which can accelerate the convergence of the residuals over same mesh scale and has higher resolution of the flow. Based on OpenFOAM with DG method, the ratio of overhead in equations discretization stage increases, especially when solving Euler equations using an explicit method. The equations discretization stage has a better potential parallelism than the other two stages due to no existence of communication. In this paper, we will analysis the difference of time cost in these three stages between original OpenFOAM and OpenFOAM with DG method. By decoupling these three stages, a hybrid parallel algorithm for solving PDEs is proposed and implemented based on OpenFOAM with DG method. The experimental results show that the simulation time is reduced by 16%, and the relative speedup of the hybrid parallel algorithm is up to 2.88 compared to the original parallel algorithm with the same degree of parallelism.