A discontinuous Galerkin method for laminar low Mach number flows

Kurzfassung

In this paper we present a Discontinuous Galerkin (DG) method designed to improve the accuracy and efficiency of laminar flow simulations at low Mach numbers using a fully implicit scheme. The algorithm is based on the flux preconditioning approach, which modifies only the dissipative terms of the numerical flux. This formulation is quite simple to implement in existing implicit DG codes, it overcomes the time-stepping restrictions of explicit multistage algorithms, is consistent in time and thus applicable to unsteady flows. The performance of the method is demonstrated by solving a laminar flow past a NACA0012 airfoil at different low Mach numbers using various degrees of polynomial approximations. Computations with and without flux preconditioning are performed on different grid topologies to analyze the influence of the spatial discretization on the accuracy of the DG solutions at low Mach numbers.