A finite element solver for stationary and incompressible Navier-Stokes equations

With this paper, originally published in the EnginSoft newsletter, and also published in a preliminary release on the official Scilab site, we want to show how it is possible to tackle non trivial simulation problems.

Many people erroneously think that Scilab is just a big simple “calculator”; in reality it is a very powerful tool which allows to develop, thanks to its numerous functionalities, advanced and valuable applications which can be used in an industrial context.

We considered the Navier Stokes equations, used to model the mechanics of fluids, whose numerical solution is universally believed to be a serious and difficult task. For sake of simplicity, we decided to focus on planar, stationary and incompressible fluid motions disregarding turbulence.

We worked out some Scilab functions which opportunely called allowed us to solve three different benchmarks proposed very often in literature to test solvers. The agreement between the obtained results and the reference solutions is always very good, showing the reliability of our solver.

For the model set-up (geometry, construction, meshing, managing boundary conditions, etc…) we used gmsh (http://geuz.org/gmsh/), another useful open source software.

Do not hesitate to contact us for more information.