Characteristic Boundary Conditions for the Numerical Solution of Euler Equations by the Discontinuous Galerkin Methods

We present artificial boundary conditions for the numerical simulation of nonlinear Euler equations with the discontinuous Galerkin (DG) finite element method. The construction of the proposed boundary conditions is based on characteristic analysis which follows the Euler equations and are applied for boundaries with arbitrary shape and orientation. Numerical experiments demonstrate that the proposed boundary treatment enables to convect out of the computational domain complex flow features with little distortion. In addition, it is shown that small-amplitude acoustic disturbances could be convected out of the computational domain, with no significant deterioration of the overall accuracy of the method.