Maximum-principle-satisfying High Order Finite Volume Weighted Essentially Nonoscillatory Schemes for Convection-diffusion Equations

Authors:
Xiangxiong Zhang;Yuanyuan Liu;Chi-Wang Shu
Affiliations:
zhangxx@dam.brown.edu;xiaoliu@mail.ustc.edu.cn;shu@dam.brown.edu
Venue:
SIAM Journal on Scientific Computing
Year:
2012

Citing 13
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Abstract

To easily generalize the maximum-principle-satisfying schemes for scalar conservation laws in [X. Zhang and C.-W. Shu, J. Comput. Phys., 229 (2010), pp. 3091-3120] to convection diffusion equations, we propose a nonconventional high order finite volume weighted essentially nonoscillatory (WENO) scheme which can be proved maximum-principle-satisfying. Two-dimensional extensions are straightforward. We also show that the same idea can be used to construct high order schemes preserving the maximum principle for two-dimensional incompressible Navier-Stokes equations in the vorticity stream-function formulation. Numerical tests for the fifth order WENO schemes are reported.