Semi implicit second order discontinuous Galerkin convection for ALE calculations

Element results are in general discontinuous across element boundaries. In the ALE method and related moving element methods convection of these data with respect to the element grid is required. The Discontinuous Galerkin Method provides an obvious choice for discretization of this convective process. In order to assure stability and accuracy at large step sizes (large values of the Courant number), the Discontinuous Galerkin method is extended to second order. This is not sufficient to obtain an attractive stability region. Therefore the equations are enriched with selective implicit terms. This results in a remarkably stable convection scheme without the use of any explicit limiting. Results are shown of a standard pure advection test problem, the Molenkamp test and of an extrusion simulation, which resembles convection with source terms