Journal of Computational Physics
The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
SIAM Journal on Numerical Analysis
Runge–Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems
Journal of Scientific Computing
Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
SIAM Journal on Numerical Analysis
Stability of W-methods with applications to operator splitting and to geometric theory
Applied Numerical Mathematics
Principles of Computational Fluid Dynamics
Principles of Computational Fluid Dynamics
Space-time discontinuous Galerkin method for the compressible Navier-Stokes equations
Journal of Computational Physics
Space-time discontinuous Galerkin method for the compressible Navier-Stokes equations
Journal of Computational Physics
hpGEM---A software framework for discontinuous Galerkin finite element methods
ACM Transactions on Mathematical Software (TOMS)
Journal of Computational Physics
Journal of Computational Physics
Spectral element method in time for rapidly actuated systems
Journal of Computational Physics
Journal of Computational Physics
Space-time discontinuous Galerkin finite element method for two-fluid flows
Journal of Computational Physics
Hi-index | 31.48 |
The space-time discontinuous Galerkin discretization of the compressible Navier-Stokes equations results in a non-linear system of algebraic equations, which we solve with pseudo-time stepping methods. We show that explicit Runge-Kutta methods developed for the Euler equations suffer from a severe stability constraint linked to the viscous part of the equations and propose an alternative to relieve this constraint while preserving locality. To evaluate its effectiveness, we compare with an implicit-explicit Runge-Kutta method which does not suffer from the viscous stability constraint. We analyze the stability of the methods and illustrate their performance by computing the flow around a 2D airfoil and a 3D delta wing at low and moderate Reynolds numbers.