Discrete compatibility in finite difference methods for viscous incompressible fluid flow
- Simon Fraser Univ., Burnaby (Canada)
- Univ. of British Columbia, Vancouver (Canada)
Thom`s vorticity condition for solving the incompressible Navier-Stokes equations is generally known as a first-order method since the local truncation error for the value of boundary vorticity is first-order accurate. In the present paper, it is shown that convergence in the boundary vorticity is actually second order for steady problems and for time-dependent problems when t > 0. The result is proved by looking carefully at error expansions for the discretization which have been previously used to show second-order convergence of interior vorticity. Numerical convergence studies confirm the results. At t = 0 the computed boundary vorticity is first-order accurate as predicted by the local truncation error, Using simple model problems for insight we predict that the size of the second-order error term in the boundary condition blows up like C/{radical}t as t {r_arrow} 0. This is confirmed by careful numerical experiments. A similar phenomenon is observed for boundary vorticity computed using a primitive method based on the staggered marker-and-cell grid. 27 refs., 15 tabs.
- OSTI ID:
- 447042
- Journal Information:
- Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: 2 Vol. 126; ISSN 0021-9991; ISSN JCTPAH
- Country of Publication:
- United States
- Language:
- English
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