On maximum-principle-satisfying high order schemes for scalar conservation laws
 作者： Xiangxiong Zhang,  Chi-Wang Shu 作者单位： 1Department of Mathematics, Brown University, Providence, RI 02912, United States2Division of Applied Mathematics, Brown University, Providence, RI 02912, United States 刊名： Journal of Computational Physics, 2009, Vol.229 (9), pp.3091-3120 来源数据库： Elsevier Journal DOI： 10.1016/j.jcp.2009.12.030 关键词： Hyperbolic conservation laws;  Finite volume scheme;  Discontinuous Galerkin method;  Essentially non-oscillatory scheme;  Weighted essentially non-oscillatory scheme;  Maximum principle;  High order accuracy;  Strong stability preserving time discretization;  Passive convection equation;  Incompressible flow; 英文摘要： Abstract(#br)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.

• scheme　略图
• conservation　保存
• principle　原理
• essentially　本质上
• oscillatory　振动的
• convection　对流
• maximum　最大值
• preserving　保藏
• order
• satisfying　饱和