An analysis of the discontinuous Galerkin method for a scalar hyperbolic equation
Mathematics of Computation
Time dependent boundary conditions for hyperbolic systems
Journal of Computational Physics
Time-dependent boundary conditions for hyperbolic systems, II
Journal of Computational Physics
Non-reflecting boundary conditions
Journal of Computational Physics
Dispersion-relation-preserving finite difference schemes for computational acoustics
Journal of Computational Physics
Accurate solutions of the Navier-Stokes equations despite unknown outflow boundary data
Journal of Computational Physics
Journal of Computational Physics
Applied Numerical Mathematics
The Runge-Kutta discontinuous Galerkin method for conservation laws V multidimensional systems
Journal of Computational Physics
A super-grid-scale model for simulating compressible flow on unbounded domains
Journal of Computational Physics
A Discontinuous Galerkin Method for Linear Symmetric Hyperbolic Systems in Inhomogeneous Media
Journal of Scientific Computing
Journal of Computational Physics
Analysis of sponge zones for computational fluid mechanics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
A high-order super-grid-scale absorbing layer and its application to linear hyperbolic systems
Journal of Computational Physics
Journal of Computational Physics
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We present artificial boundary conditions for the numerical simulation of compressible flows using high-order accurate discretizations with the discontinuous Galerkin (DG) finite element method. The construction of the proposed boundary conditions is based on characteristic analysis and 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. Furthermore, it was found that application of the proposed boundary treatment for viscous flow over a cylinder yields superior performance compared to simple extrapolation methods.