Essential compact scheme for unsteady viscous incompressible flows

Weinan E Institute for Advanced Study Jian-Guo Liu Temple University

Numerical Analysis and Scientific Computing mathscidoc:1702.25068

Journal of Computational Physics, 126, (1), 122-138, 1996.6
A new fourth-order accurate finite difference scheme for the computation of unsteady viscous incompressible flows is introduced. The scheme is based on the vorticity-stream function formulation. It is essentially compact and has the nice features of a compact scheme with regard to the treatment of boundary conditions. It is also very efficient, at every time step or Runge–Kutta stage, only two Poisson-like equations have to be solved. The Poisson-like equations are amenable to standard fast Poisson solvers usually designed for second order schemes. Detailed comparison with the second-order scheme shows the clear superiority of this new fourth-order scheme in resolving both the boundary layers and the gross features of the flow. This efficient fourth-order scheme also made it possible to compute the driven cavity flow at Reynolds number 106on a 10242grid at a reasonable cost. Fourth-order convergence is proved under mild regularity requirements. This is the first such result to our knowledge
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  title={Essential compact scheme for unsteady viscous incompressible flows},
  author={Weinan E, and Jian-Guo Liu},
  booktitle={Journal of Computational Physics},
Weinan E, and Jian-Guo Liu. Essential compact scheme for unsteady viscous incompressible flows. 1996. Vol. 126. In Journal of Computational Physics. pp.122-138.
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