Advanced study for the numerical resolution of the navier-stokes equations using the fractional step method

Abstract

Different aspects related to Computational Fluid Dynamics (CDF) will be studied. First, theoretical aspects needed for the resolution of this kind of problems with the finite element method are reviewed. Then, the heat equation is also reviewed. After that, the generic convection diffusion equation is studied, and different convective schemes are used (CDS, UDS, SUDS and QUICK). Numerical experiments are conducted to compare them between each other. Then the problems that arise when trying to numerically solve the Navier Stokes equations are reviewed. These include the checkerboard problem and the fact the the equations are highly coupled. The equations will be solved for different cases, amongst them the Lid-Driven Cavity, using the convective schemes studied previously with a collocated mesh and a fractional step method. Finally, the energy equation is coupled with the Navier-Stokes equations, where the body forces that were previously neglected are also added. This allows the simulation of natural convection cases. The cases studied is that of a cavity with walls at different temperatures, which causes the fluid motion. This case is solved with a Staggered Mesh