A parallel implementation of an implicit discontinuous Galerkin finite element scheme for fluid flow problems

The discontinuous Galerkin (DG) method is frequently used in computational fluid dynamics for its stability and high order of accuracy. A disadvantage of the DG method is its high computational demands. The aim of this paper is to weaken this drawback by means of parallelization of the DG algorithm. The computation is performed on a network of computers with distributed memory using the Java Remote Method Invocation, which is included in the Java programming language. The partition of the boundary value problem into n subproblems, which is then solved by n computers separately, is based on the overlapping Schwarz method. On basis of physical nature of the problem, the present paper proposes minimal size of the overlap that allows for only one Schwarz iteration thereby increasing efficiency of parallelization. The scalability and efficiency of the presented parallelization approach is demonstrated on several test problems. In order to stabilize the DG method in presence of shocks, a recently developed technique by Huerta et al. (Int. J. Numer. Meth. Fluids 69(10), 2012, 1614-1632), which introduces discontinuities in basis functions in regions with a shock, is adopted here. A modification of this approach, which lowers the computational and implementational demands, is presented here.