Finite Difference Methods for 3D Viscous Incompressible Flows in the Vorticity-Vector Potential Formulation on Nonstaggered Grids

Weinan E, Jian Guo Liu

Research output: Contribution to journalArticle

38 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)57-82
Number of pages26
JournalJournal of Computational Physics
Volume138
Issue number1
DOIs
StatePublished - Nov 15 1997
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

Fingerprint Dive into the research topics of 'Finite Difference Methods for 3D Viscous Incompressible Flows in the Vorticity-Vector Potential Formulation on Nonstaggered Grids'. Together they form a unique fingerprint.

  • Cite this