A staggered-grid finite volume method for the vorticity-velocity equations

This paper provides a novel finite volume technique for solving two-dimensional viscous steady flows using the vorticity-velocity equations written as a second-order system. The parabolic vorticity transport equation and the elliptic equations for the velocity components are discretized in time using a two level implicit Euler scheme and in space using a staggered-grid finite volume discretization. A line-Gauss-Seidel iteration combined with a deferred-correction procedure is used to drive to zero the steady-state residuals, which are second-order accurate and satisfy exactly the finite volume discrete forms of the continuity equation and of the vorticity definition. The accuracy and general applicability of the method are demonstrated vs a few model problems using orthogonal as well as nonorthogonal grids.