On maximum-principle-satisfying high order schemes for scalar conservation laws
On maximum-principle-satisfying high order schemes for scalar conservation laws
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DOI：
10.1016/j.jcp.2009.12.030
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发表时间：
2010-05
期刊：
影响因子：
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通讯作者：
Xiangxiong Zhang;Chi-Wang Shu
中科院分区：
文献类型：
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作者：
Xiangxiong Zhang;Chi-Wang Shu
构造了标量守恒律的满足严格极大值原理的一致高阶精度格式。建立了求解一维标量守恒律方程的有限体积格式（如ENO格式或韦诺格式）或间断Galerkin格式（DG格式）的一阶Euler前向离散的限制器的一般框架（对于任意精度阶）.强保稳定高阶时间离散化将保持最大值原理。它是直接的方法扩展到二维和更高的维度上的矩形网格。我们还表明，相同的限制器可以保持DG或有限体积方案求解二维不可压缩欧拉方程的涡量流函数制定的最大值原理，或任何被动对流方程与不可压缩的速度场。数值试验的韦诺有限体积格式和DG方法的报告。
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.