Stable boundary conditions and difference schemas for Navier-Stokes equations
SIAM Journal on Numerical Analysis
Efficient implementation of essentially non-oscillatory shock-capturing schemes
Journal of Computational Physics
Numerical computation of internal & external flows: fundamentals of numerical discretization
Numerical computation of internal & external flows: fundamentals of numerical discretization
Journal of Computational Physics
Artificial boundary conditions for incompletely parabolic perturbations of hyperbolic systems
SIAM Journal on Mathematical Analysis
A Stable Penalty Method for the Compressible Navier--Stokes Equations: I. Open Boundary Conditions
SIAM Journal on Scientific Computing
Journal of Computational Physics
The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
SIAM Journal on Numerical Analysis
Strong stability preserving high-order time discretization methods
Strong stability preserving high-order time discretization methods
Journal of Computational and Applied Mathematics
Journal of Computational Physics
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A study of boundary and interface conditions for Discontinuous Galerkin approximations of fluid flow equations is undertaken in this paper. While the interface flux for the inviscid case is usually computed by approximate Riemann solvers, most discretizations of the Navier-Stokes equations use an average of the viscous fluxes from neighboring elements. The paper presents a methodology for constructing a set of stable boundary/interface conditions that can be thought of as "viscous" Riemann solvers and are compatible with the inviscid limit.