High order boundary conditions for flow simulations in vorticity-velocity formulation

This thesis is focused on the different possiblities to calculate the vorticity at the wall when solving Navier-Stokes equations in vorticity-velocity formulation. Many formulas already exist for that effect. The aim will be to investigate high order boundary conditions. The developed formula is obtained by following the Woods method but with one level more information. This formula is then compared to other known formulas by testing them on one- and two-dimensional cases. To calculate the error for each case, we need a reference solution. In 1D, we use the analytical solution for the constant pressure gradient in a channel that we developed in this thesis. For the 2D case, as there is no analytical solution in a channel, we do a self converging test on the backward facing step case. The goal is to compare the error given by these different formulas and compare their accuracy. The case of a dipole in a Poiseuille flow was also solved in order to provide numerical results.