Unsteady Discontinuous Galerkin Method of a High Order of Accuracy for Modeling Turbulent Flows

Abstract

This paper presents a brief description of the Zhukovsky Central Aerohydrodynamic Institute (TsAGI) code based on the Galerkin method of a high order of accuracy with discontinuous basic functions. The functions is reconstructed for conservative variables. Gradients of the variables are determined using the Bassi–Rebay 2 method. For integrating, the Gaussian quadrature rules are used. The coordinates are transformed by serendipian elements. In computing by schemes of an order higher than the second order, the curvature of grid lines is taken into account. A comparison with finite volume methods is performed, including the WENO method with constant weights and a single quadrature point on a cell face. The classical tests are used, namely, a subsonic flow around a circular cylinder in an ideal gas, the diagonal convection of a two-dimensional isentropic vortex, and the decay of the Taylor–Green vortex.