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

In this work we present a discontinuous Galerkin (DG) method designed to improve the accuracy and efficiency of the steady-state solution at very low Mach number flows using an explicit scheme. The algorithm is based on a perturbed formulation of the compressible Euler equations 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 scheme is demonstrated by solving an inviscid flow past a NACA0012 airfoil at different very low Mach numbers using various degrees of polynomial approximation. 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.