Runge–Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems
Journal of Scientific Computing
Numerical Comparison of WENO Finite Volume and Runge–Kutta Discontinuous Galerkin Methods
Journal of Scientific Computing
Shock detection and limiting with discontinuous Galerkin methods for hyperbolic conservation laws
Applied Numerical Mathematics - Special issue: Workshop on innovative time integrators for PDEs
A Fast and Stable Well-Balanced Scheme with Hydrostatic Reconstruction for Shallow Water Flows
SIAM Journal on Scientific Computing
Journal of Scientific Computing
SIAM Journal on Scientific Computing
Journal of Computational Physics
Space-time discontinuous Galerkin discretization of rotating shallow water equations
Journal of Computational Physics
Journal of Computational Physics
A Performance Comparison of Continuous and Discontinuous Finite Element Shallow Water Models
Journal of Scientific Computing
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This work extends a well-balanced second-order Runge-Kutta discontinuous Galerkin (RKDG2) scheme to provide conservative simulations for shallow flows involving wetting and drying over irregular topographies with friction effects. For this purpose, a wetting and drying technique designed originally for a finite volume (FV) scheme is improved and implemented, which includes the discretization of friction source terms via a splitting implicit integration approach. Another focus of this work is to design a fully conserved RKDG2 scheme to provide conservative solutions for both mass and momentum through a local slope limiting process. Several steady and transient benchmark tests with/without friction effects are simulated to validate the new solver and demonstrate the effects of different slope limiting processes, i.e. globally and locally slope limiting processes.