Simplified second-order Godunov-type methods
SIAM Journal on Scientific and Statistical Computing
Error estimates for finite element methods for scalar conservation laws
SIAM Journal on Numerical Analysis
Average-state Jacobians and implicit methods for compressible viscous and turbulent flows
Journal of Computational Physics
On the Choice of Wavespeeds for the HLLC Riemann Solver
SIAM Journal on Scientific Computing
High-order accurate discontinuous finite element solution of the 2D Euler equations
Journal of Computational Physics
The Runge-Kutta discontinuous Galerkin method for conservation laws V multidimensional systems
Journal of Computational Physics
Journal of Computational Physics
A problem-independent limiter for high-order Runge—Kutta discontinuous Galerkin methods
Journal of Computational Physics
Runge–Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems
Journal of Scientific Computing
Discontinuous Galerkin Methods: Theory, Computation and Applications
Discontinuous Galerkin Methods: Theory, Computation and Applications
Journal of Computational Physics
Journal of Scientific Computing
Journal of Scientific Computing
Space-time discontinuous Galerkin method for the compressible Navier-Stokes equations
Journal of Computational Physics
Journal of Computational Physics
Space-time discontinuous Galerkin method for advection-diffusion problems on time-dependent domains
Applied Numerical Mathematics
Space-time discontinuous Galerkin finite element method for shallow water flows
Journal of Computational and Applied Mathematics
Space-time discontinuous Galerkin method for nonlinear water waves
Journal of Computational Physics
On a robust discontinuous Galerkin technique for the solution of compressible flow
Journal of Computational Physics
hpGEM---A software framework for discontinuous Galerkin finite element methods
ACM Transactions on Mathematical Software (TOMS)
Space-time discontinuous Galerkin discretization of rotating shallow water equations
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Spectral element method in time for rapidly actuated systems
Journal of Computational Physics
Finite volume schemes of very high order of accuracy for stiff hyperbolic balance laws
Journal of Computational Physics
An adaptive multitime multigrid algorithm for time-periodic flow simulations
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
A space--time discontinuous Galerkin method for the time-dependent Oseen equations
Applied Numerical Mathematics
Very high order PNPM schemes on unstructured meshes for the resistive relativistic MHD equations
Journal of Computational Physics
Discontinuous Galerkin solution of compressible flow in time-dependent domains
Mathematics and Computers in Simulation
Space-time discontinuous Galerkin finite element method for two-fluid flows
Journal of Computational Physics
WENO schemes on arbitrary mixed-element unstructured meshes in three space dimensions
Journal of Computational Physics
Numerical simulation of inviscid compressible flow by higher order numerical schemes
ACMOS'06 Proceedings of the 8th WSEAS international conference on Automatic control, modeling & simulation
Journal of Computational Physics
A space-time discontinuous Galerkin method for the incompressible Navier-Stokes equations
Journal of Computational Physics
Hi-index | 31.55 |
A new space-time discontinuous Galerkin finite element method for the solution of the Euler equations of gas dynamics in time-dependent flow domains is presented. The discontinuous Galerkin discretization results in an efficient elementwise conservative upwind finite element method, which is particularly well suited for local mesh refinement. The upwind scheme uses a formulation of the HLLC flux applicable to moving meshes and several formulations for the stabilization operator to ensure that monotone solutions around discontinuities are investigated. The non-linear equations of the space-time discretization are solved using a multigrid accelerated pseudo-time-integration technique with an optimized Runge-Kutta method. The linear stability of the pseudo-time-integration method is investigated for the linear advection equation. The numerical scheme is demonstrated with simulations of the flow field in a shock tube, a channel with a bump, and an oscillating NACA 0012 airfoil. These simulations show that using the data at the superconvergence points, the accuracy of the numerical discretization is O(h5/2) in space for smooth subsonic flows, both on structured and on locally refined meshes, and that the space-time adaptation can significantly improve the accuracy and efficiency of the numerical method.