Maximum-principle-satisfying high order finite volume weighted essentially nonoscillatory schemes for convection-diffusion equations

Xiangxiong Zhang Brown University Yuanyuan Liu University of Science and Technology of China Chi-Wang Shu Brown University

Numerical Analysis and Scientific Computing mathscidoc:1610.25075

SIAM Journal on Scientific Computing, 34, A627-A658, 2012
To easily generalize the maximum-principle-satisfying schemes for scalar conservation laws to convection diffusion equations, we propose a non-conventional high order finite volume weighted essentially non-oscillatory (WENO) scheme which can be proven 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.
convection diffusion equations; finite volume scheme; weighted essentially non-oscillatory scheme; maximum principle; high order accuracy; strong stability preserving time discretization; incompressible flow; Navier-Stokes equations
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@inproceedings{xiangxiong2012maximum-principle-satisfying,
  title={Maximum-principle-satisfying high order finite volume weighted essentially nonoscillatory schemes   for convection-diffusion equations},
  author={Xiangxiong Zhang, Yuanyuan Liu, and Chi-Wang Shu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161012112130370200193},
  booktitle={SIAM Journal on Scientific Computing},
  volume={34},
  pages={A627-A658},
  year={2012},
}
Xiangxiong Zhang, Yuanyuan Liu, and Chi-Wang Shu. Maximum-principle-satisfying high order finite volume weighted essentially nonoscillatory schemes for convection-diffusion equations. 2012. Vol. 34. In SIAM Journal on Scientific Computing. pp.A627-A658. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161012112130370200193.
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