Total-variation-diminishing time discretizations
SIAM Journal on Scientific and Statistical Computing
A finite-volume high-order ENO scheme for two-dimensional hyperbolic systems
Journal of Computational Physics
Runge–Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems
Journal of Scientific Computing
A technique of treating negative weights in WENO schemes
Journal of Computational Physics
ADER: Arbitrary High Order Godunov Approach
Journal of Scientific Computing
ADER schemes for three-dimensional non-linear hyperbolic systems
Journal of Computational Physics
Journal of Computational Physics
ADER schemes for the shallow water equations in channel with irregular bottom elevation
Journal of Computational Physics
Solvers for the high-order Riemann problem for hyperbolic balance laws
Journal of Computational Physics
Journal of Computational Physics
ADER finite volume schemes for nonlinear reaction--diffusion equations
Applied Numerical Mathematics
Journal of Computational Physics
High order multi-moment constrained finite volume method. Part I: Basic formulation
Journal of Computational Physics
Journal of Computational Physics
WENO schemes on arbitrary mixed-element unstructured meshes in three space dimensions
Journal of Computational Physics
Adaptive ADER Methods Using Kernel-Based Polyharmonic Spline WENO Reconstruction
SIAM Journal on Scientific Computing
Journal of Computational and Applied Mathematics
Comparison of solvers for the generalized Riemann problem for hyperbolic systems with source terms
Journal of Computational Physics
The generalized Riemann problems for compressible fluid flows: Towards high order
Journal of Computational Physics
Hi-index | 31.50 |
In this paper, we first briefly review the semi-analytical method [E.F. Toro, V.A. Titarev, Solution of the generalized Riemann problem for advection-reaction equations, Proc. Roy. Soc. London 458 (2018) (2002) 271-281] for solving the derivative Riemann problem for systems of hyperbolic conservation laws with source terms. Next, we generalize it to hyperbolic systems for which the Riemann problem solution is not available. As an application example we implement the new derivative Riemann solver in the high-order finite-volume ADER advection schemes. We provide numerical examples for the compressible Euler equations in two space dimensions which illustrate robustness and high accuracy of the resulting schemes.