Higher-order time integration with a local Lax–Wendroff procedure for a central scheme on an overlapping grid

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.