A new version of the two-dimensional Lax-Friedrichs scheme. (English) Zbl 0829.35076
Summary: We develop a new two-dimensional version of the Lax-Friedrichs scheme, which corresponds exactly to a transport projection method. The scheme we obtain in this way is different from the one derived by averaging the one-dimensional scheme in the two directions as usually done. The Lax-Friedrichs scheme is known to be a very stable scheme with much diffusion. However, this diffusion can be easily reduced by using corrected fluxes, without altering the total-variation estimates. The accuracy of this corrected scheme is of order two except near a local extrema. The numerical results computed by using this corrected scheme are similar to the ones obtained by using the Godunov scheme with corrected fluxes but require less CPU time. Convergence towards the entropy solution is proved, and some extensions to systems of conservation laws or three-dimensional models are discussed. Some numerical experiments are reported.
MSC:
| 35L65 | Hyperbolic conservation laws |
| 65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |
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