Space-time discontinuous Galerkin finite element method with dynamic grid motion for inviscid compressible flows II. Efficient flux quadrature

A new and efficient quadrature rule for the flux integrals arising in the space–time discontinuous Galerkin discretization of the Euler equations in a moving and deforming space–time domain is presented and analyzed. The quadrature rule is a factor three more efficient than the commonly applied quadrature rule and does not affect the local truncation error and stability of the numerical scheme. The local truncation error of the resulting numerical discretization is determined and is shown to be the same as when product Gauss quadrature rules are used. Details of the approximation of the dissipation in the numerical flux are presented, which render the scheme consistent and stable. The method is successfully applied to the simulation of a three-dimensional, transonic flow over a deforming wing