Comparing the Solution of the Navier-Stokes Equations Using a Fixed Point Iterative Method and Using COMSOL Multiphysics

Blanca Bermúdez Juárez, Beatriz Bonilla Capilla, José David Alanis Urquieta, Alejandro Rangel Huerta, Wuiyebaldo Fermín Guerrero Sanchez

In this paper, we compare the solutions for the Navier-Stokes equations with moderate and very high Reynolds numbers obtained using a Fixed Point Iterative Method with those obtained using COMSOL Multiphysics. Despite the advantages of COMSOL, we want to show that our results, using a Fixed Point Iterative method agree as much as possible, with those obtained with COMSOL. Results for viscous incompressible flows in 2D are presented, using the Stream Function-vorticity formulation of the Navier-Stokes equations. The Fixed point Iterative Method uses Finite Differences and a uniform mesh; COMSOL uses the Finite Element Method and the formulation in primitive variables and the mesh is refined in some places; streamline and crosswind diffusion are also used. Results are reported, in the case of the lid-driven cavity problem for Reynolds numbers in the range of 5000 ≤ Re ≤ 100000.

As the Reynolds number increases, the time and the step mesh have to be refined, both for time and space in order to capture the fast dynamics of the flow and numerically, because of stability reasons. The advantages of our code are: it is “transparent” and easily modifiable, so, it can be used for solving other problems. We are looking forward to parallelize it.

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