## Finite difference schemes for incompressible flow based on local pressure boundary conditions

Publication ,  Journal Article
Johnston, H; Liu, JG
Published in: Journal of Computational Physics
July 20, 2002

In this paper we discuss the derivation and use of local pressure boundary conditions for finite difference schemes for the unsteady incompressible Navier-Stokes equations in the velocity-pressure formulation. Their use is especially well suited for the computation of moderate to large Reynolds number flows. We explore the similarities between the implementation and use of local pressure boundary conditions and local vorticity boundary conditions in the design of numerical schemes for incompressible flow in 2D. In their respective formulations, when these local numerical boundary conditions are coupled with a fully explicit convectively stable time stepping procedure, the resulting methods are, simple to implement and highly efficient. Unlike the vorticity formulation, the use of the local pressure boundary condition approach is readily applicable to 3D flows. The simplicity of the local pressure boundary condition approach and its easy adaptation to more general flow settings make the resulting scheme an attractive alternative to the more popular methods for solving the Navier-Stokes equations in the velocity-pressure formulation. We present numerical results of a second-order finite difference scheme on a nonstaggered grid using local pressure boundary conditions. Stability and accuracy of the scheme applied to Stokes flow is demonstrated using normal mode analysis. Also described is the extension of the method to variable density flows. © 2002 Elsevier Science (USA).

## Published In

Journal of Computational Physics

0021-9991

July 20, 2002

180

1

## Start / End Page

120 / 154

• Applied Mathematics
• 51 Physical sciences
• 49 Mathematical sciences
• 40 Engineering
• 09 Engineering
• 02 Physical Sciences
• 01 Mathematical Sciences

### Citation

APA
Chicago
ICMJE
MLA
NLM
Johnston, H., & Liu, J. G. (2002). Finite difference schemes for incompressible flow based on local pressure boundary conditions. Journal of Computational Physics, 180(1), 120–154. https://doi.org/10.1006/jcph.2002.7079
Johnston, H., and J. G. Liu. “Finite difference schemes for incompressible flow based on local pressure boundary conditions.” Journal of Computational Physics 180, no. 1 (July 20, 2002): 120–54. https://doi.org/10.1006/jcph.2002.7079.
Johnston H, Liu JG. Finite difference schemes for incompressible flow based on local pressure boundary conditions. Journal of Computational Physics. 2002 Jul 20;180(1):120–54.
Johnston, H., and J. G. Liu. “Finite difference schemes for incompressible flow based on local pressure boundary conditions.” Journal of Computational Physics, vol. 180, no. 1, July 2002, pp. 120–54. Scopus, doi:10.1006/jcph.2002.7079.
Johnston H, Liu JG. Finite difference schemes for incompressible flow based on local pressure boundary conditions. Journal of Computational Physics. 2002 Jul 20;180(1):120–154.

## Published In

Journal of Computational Physics

0021-9991

July 20, 2002

180

1

120 / 154