Title of article :
On maximum-principle-satisfying high order schemes for scalar conservation laws
Author/Authors :
Zhang، نويسنده , , Xiangxiong and Shu، نويسنده , , Chi-Wang، نويسنده ,
Issue Information :
روزنامه با شماره پیاپی سال 2010
Pages :
30
From page :
3091
To page :
3120
Abstract :
We construct uniformly high order accurate schemes satisfying a strict maximum principle 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 maximum 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 incompressible velocity field. Numerical tests for both the WENO finite volume scheme and the DG method are reported.
Keywords :
Discontinuous Galerkin Method , Essentially non-oscillatory scheme , Weighted essentially non-oscillatory scheme , High order accuracy , Incompressible Flow , Passive convection equation , hyperbolic conservation laws , Maximum principle , Finite volume scheme , Strong stability preserving time discretization
Journal title :
Journal of Computational Physics
Serial Year :
2010
Journal title :
Journal of Computational Physics
Record number :
1482250
Link To Document :
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