Discontinuous Galerkin solution of preconditioned Euler equations for very low Mach number flows

Kurzfassung

In this work we present a Discontinuous Galerkin (DG) method designed to improve the accuracy and efficiency of the solution at very low Mach number flows using an explicit scheme for the temporal discretization of the compressible Euler equations. The algorithm is based on a perturbed formulation of the governing equ ations and employs the preconditioning of both the instationary term of the governing equations and the dissipative term of the numerical flux function (full preconditioning approach). The performance of the method is demonstrated by solving an inviscid flow past a NACA0012 airfoil at different very low Mach numbers using various degrees of polynomial approximations. We present numerical results computed with and without perturbed variables which illustrate the influence of the cancellation errors on both the convergence and the accuracy of the DG solutions at low Mach numbers.