Essentially compact schemes for unsteady viscous incompressible flows (Q1917114)

A new fourth-order accurate finite difference scheme for the computation of unsteady viscous incompressible flows is introduced. The scheme is based on the vorticity-stream function formulation. It is essentially compact and has the nice features of a compact scheme with regard to the treatment of boundary conditions. At every time step or Runge-Kutta stage, only two Poisson-like equations have to be solved. This scheme is applied to the driven cavity flow at Reynolds number \(10^6\) on a \(1024^2\) grid at a reasonable cost. Fourth order convergence is proved under mild regularity requirements.