Maximum-principle-satisfying High Order Finite Volume Weighted Essentially Nonoscillatory Schemes for Convection-diffusion Equations
Name
Zhang-2012-MAXIMUM-PRINCIPLE-SATISFYING HIGH.pdf
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1.34 MB
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Author(s)
Zhang, Xiangxiong
Liu, Yuanyuan
Shu, Chi-Wang
Date Issued
March 2012
Journal
SIAM Journal on Scientific Computing
Publisher
Society for Industrial and Applied Mathematics
Citation
Zhang, Xiangxiong, Yuanyuan Liu, and Chi-Wang Shu. “Maximum-principle-satisfying High Order Finite Volume Weighted Essentially Nonoscillatory Schemes for Convection-diffusion Equations.” SIAM Journal on Scientific Computing 34.2 (2012): A627. Copyright © 2012 Society for Industrial and Applied Mathematics
Version
Final published version
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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DOI of Published Version
https://doi.org/10.1137/110839230
