Discrete compatibility in finite difference methods for viscous incompressible fluid flow (Q1924708)

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.