A two-step monolithic method for the efficient simulation of incompressible flows

We propose a simple technique for improving computationally the efficiency of monolithic velocity-pressure solvers for incompressible flow problems. The idea consists in solving the discrete nonlinear system of governing equations in two steps: introducing artificial' compressibility first and afterwards correcting the solution by solving the original incompressible system. The speed-up is obtained because of a better conditioning of the modified discrete system solved at the prediction step. The formulation can be easily implemented into existing monolithic codes requiring minor modification only. The paper concludes with two examples validating the formulation and facilitating the estimation of the obtained speed-up. For the tests chosen, an average speed-up is approximately double, suggesting that the method is a feasible approach for incompressible flows' simulation. Copyright (c) 2014 John Wiley & Sons, Ltd.