High-order implicit palindromic discontinuous Galerkin method for kinetic-relaxation approximation

•Matrix-free with StarPu parallelization DG scheme for advection.•CFL-free and Matrix-free DG scheme for hyperbolic conservation laws.•High-order expansion in time with symmetric methods.•Application to 2D/3D fluid flows on non Cartesian geometries. We construct a high order discontinuous Galerkin method for solving general hyperbolic systems of conservation laws. The method is CFL-less, matrix-free, has the complexity of an explicit scheme and can be of arbitrary order in space and time. The construction is based on: (a) the representation of the system of conservation laws by a kinetic vectorial representation with a stiff relaxation term; (b) a matrix-free, CFL-less implicit discontinuous Galerkin transport solver; and (c) a stiffly accurate composition method for time integration. The method is validated on several one-dimensional test cases. It is then applied on two-dimensional and three-dimensional test cases: flow past a cylinder, magnetohydrodynamics and multifluid sedimentation.