Discrete Compatibility in Finite Difference Methods for Viscous Incompressible Fluid Flow
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文摘
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 whent> 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. Att