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

• Autores: Shengtai Li
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 236, Nº 18, 2012 (Ejemplar dedicado a: FEMTEC 2011: 3rd International Conference on Computational Methods in Engineering and Science, May 9-13, 2011), págs. 4756-4761
• Idioma: inglés
• DOI: 10.1016/j.cam.2012.02.026
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• Resumen

  • 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.