Uniformly high order accurate essentially non-oscillatory schemes, 111
Journal of Computational Physics
The &Dgr; • = 0 constraint in shock-capturing magnetohydrodynamics codes
Journal of Computational Physics
A New Class of Optimal High-Order Strong-Stability-Preserving Time Discretization Methods
SIAM Journal on Numerical Analysis
ADER: A High-Order Approach for Linear Hyperbolic Systems in 2D
Journal of Scientific Computing
ADER: Arbitrary High Order Godunov Approach
Journal of Scientific Computing
Finite Difference WENO Schemes with Lax--Wendroff-Type Time Discretizations
SIAM Journal on Scientific Computing
ADER schemes for three-dimensional non-linear hyperbolic systems
Journal of Computational Physics
An unsplit Godunov method for ideal MHD via constrained transport
Journal of Computational Physics
Central schemes on overlapping cells
Journal of Computational Physics
Derivative Riemann solvers for systems of conservation laws and ADER methods
Journal of Computational Physics
An unsplit Godunov method for ideal MHD via constrained transport in three dimensions
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
A fourth-order divergence-free method for MHD flows
Journal of Computational Physics
Hi-index | 7.29 |
We have implemented a high-order Lax-Wendroff type time integration for a central scheme on an overlapping grid for conservation law problems. Using a local iterative approach presented by Dumbser et al. (JCP, 2008) [12], we extend a local high-order spatial reconstruction on each cell to a local higher-order space-time polynomial on the cell. We rewrite the central scheme in a fully discrete form to avoid volume integration in the space-time domain. The fluxes at cell interfaces are calculated directly via integrating a higher-order space-time reconstruction of the flux. We compare this approach with the corresponding multi-stage Runge-Kutta time integration (RK). Numerical results show that the new time integration is more cost-effective.