Finite difference methods for 3D viscous incompressible flows in the vorticity-vector potential formulation on non-staggered grids

Weinan E Courant Institute of Mathematical Sciences Jian-Guo Liu Temple University

Numerical Analysis and Scientific Computing mathscidoc:1702.25066

Journal of Computational Physics, 138, (1), 57–82, 1997.11
Simple, efficient, and accurate finite difference methods are introduced for 3D unsteady viscous incompressible flows in the vorticity–vector potential formulation on nonstaggered grids. Two different types of methods are discussed. They differ in the implementation of the normal component of the vorticity boundary condition and consequently the enforcement of the divergence free condition for vorticity. Both second-order and fourth-order accurate schemes are developed. A detailed accuracy test is performed, revealing the structure of the error and the effect of how the convective terms are discretized near the boundary. The influence of the divergence free condition for vorticity to the overall accuracy is studied. Results on the cubic driven cavity flow at Reynolds number 500 and 3200 are shown and compared with that of the MAC scheme.
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@inproceedings{weinan1997finite,
  title={Finite difference methods for 3D viscous incompressible flows in the vorticity-vector potential formulation on non-staggered grids},
  author={Weinan E, and Jian-Guo Liu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170209130933999928399},
  booktitle={Journal of Computational Physics},
  volume={138},
  number={1},
  pages={57–82},
  year={1997},
}
Weinan E, and Jian-Guo Liu. Finite difference methods for 3D viscous incompressible flows in the vorticity-vector potential formulation on non-staggered grids. 1997. Vol. 138. In Journal of Computational Physics. pp.57–82. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170209130933999928399.
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