Boundary conditions and estimates for the steady Stokes equations on staggered grids

被引：14

作者：

Gustafsson B. ^{[1
]}

Nilsson J. ^{[1
]}

机构：

[1] Department of Scientific Computing, Uppsala University, P.O. Box 120

来源：

Journal of Scientific Computing | 2000年 / 15卷 / 01期

关键词：

Boundary conditions; Staggered grids; Stokes equations;

D O I：

10.1023/A:1007545718304

中图分类号：

学科分类号：

摘要：

We consider the steady state Stokes equations, describing low speed flow and derive estimates of the solution for various types of boundary conditions. We formulate the boundary conditions in a new way, such that the boundary value problem becomes non-singular. By using a difference approximation on a staggered grid we are able to derive a non-singular approximation in a direct way. Furthermore, we derive the same type of estimates as for the continuous case. Numerical experiments confirm the theoretical results.

引用

页码：29 / 59

页数：30

共 8 条

[1]

Abdallah, S., Numerical solution for the pressure Poisson equation with Neumann boundary conditions using a non-staggered grid, I (1987) J. Comput. Phys., 70, pp. 182-192

[2]

Barrett, R., Berry, M., Chan, T.F., Demmel, J., Donato, J., Dongarra, J., Eijkhout, V., Van der Vorst, H., (1994) Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods, , SIAM, Philadelphia, PA

[3]

Gustafsson, B., Nilsson, J., Fourth order methods for the Stokes and Navier-Stokes equations on staggered grids (2000) Frontiers of Computational Fluid Dynamics

[4]

Harlow, F.H., Welch, J.E., Numerical calculation of time-dependent viscous incompressible flow of fluid with a free surface (1965) Phys. Fluids, 8, pp. 2181-2189

[5]

Morinishi, Y., Lund, T.S., Vasilyev, O.V., Moin, P., Fully conservative higher order finite difference schemes for incompressible flow (1998) J. Comp. Phys., 143, pp. 90-124

[6]

Strikwerda, J.C., Finite difference methods for the stokes and Navier-Stokes equations (1984) SIAM J. Sci. Stat. Comput., 5, pp. 56-68

[7]

Tau, E.Y., Numerical solution of the steady Stokes equations (1992) J. Comput. Phys., 90, pp. 190-195

[8]

Wesseling, P., Segal, A., Kassels, C.G.M., Computing flows on general three-dimensional nonsmooth staggered grids (1999) J. Comp. Phys., 149, pp. 333-362

← 1 →