Identifier: 2009-36
Author(s): X. Zhang and C.-W. Shu
Title: On maximum-principle-satisfying high order schemes for scalar conservation laws
Page count: 58 pp.
Date: 2009-10-27
Abstract:
We construct uniformly high order accurate schemes satisfying a strict maximum prin- ciple for scalar conservation laws. A general framework (for arbitrary order of accuracy) is established to construct a limiter for finite volume schemes (e.g. essentially non-oscillatory (ENO) or weighted ENO (WENO) schemes) or discontinuous Galerkin (DG) method with first order Euler forward time discretization solving one dimensional scalar conservation laws. Strong stability preserving (SSP) high order time discretizations will keep the maxi- mum principle. It is straightforward to extend the method to two and higher dimensions on rectangular meshes. We also show that the same limiter can preserve the maximum principle for DG or finite volume schemes solving two-dimensional incompressible Euler equations in the vorticity stream-function formulation, or any passive convection equation with an in- compressible velocity field. Numerical tests for both the WENO finite volume scheme and the DG method are reported.
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