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

  • Authors:
  • Shengtai Li

  • Affiliations:
  • -

  • Venue:
  • Journal of Computational and Applied Mathematics
  • Year:
  • 2012

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Abstract

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.