Parallel implementation of discontinuous Galerkin method for
compressible flow simulations

Michal Zajac, Vit Dolejsi

We deal with a numerical simulation of viscous compressible flows,
which is described by the compressible Navier-Stokes equations. We
employ the discontinuous Galerkin finite element method (DGFEM), which
is based on a piecewise polynomial but discontinuous approximations.
Among several advantages of DGFEM, a favourable property is the same
stencil for any order of accuracy which is important for the parallel
efficiency of the method since the communication between cells is
carried out only trough common surfaces. We develop a parallel
implementation of the DGFEM for the Navier-Stokes equations. In the
first stage we employ the PETSc library for the parallel solution of
the corresponding linear algebra solvers. We present a set of
numerical experiments, which demonstrate an efficiency of the
developed code and also give some hints for further research.