A fractional-step method for steady-state flow

Abstract A fractional step method for solving the steady-state, incompressible, Navier-Stokes equations is presented. The proposed iterative method uses an estimate for the optimal under-relaxation coefficient at each iteration. This estimate uses prior information that is already available in the iterative method so the calculation has negligible cost. Numerical tests show that the convergence rate of the fractional step method using this optimal relaxation parameter is nearly independent of the mesh size, resulting in significant cost savings for problems with fine meshes. The ideas demonstrated in this paper are general and can be used to improve many existing iterative methods for steady flows, as well as methods for the unsteady Navier-Stokes equations and methods for other saddle-point problems.