Implementation and validation of symmetry and no-slip boundary conditions in a 3-D vortex particle-mesh method

This master thesis presents the implementation and validation of a symmetry and no-slip boundary conditions in the 3-D vortex particle-mesh (VPM) method. The first part focuses on the implementation of the no-through flow using a symmetry boundary condition. The implementation allows the diffusion through the wall, which makes it possible to study the vortex-ring reconnection at low Reynolds number ($Re_\Gamma=2000$). The second part presents how the no-slip boundary condition is implemented in the vortex particle-mesh method, which is a vorticity-velocity formulation flow solver. It presents how the required vortex sheet at the wall is computed to nullify the slip velocity. The third part is the validation of the method using two well-known results: the Poiseuille flow in a channel and the Blasius boundary layer development. The method provides almost an exact solution for the Poiseuille flow. The boundary layer develops in a channel with a slip and a no-slip wall. The flow above the boundary layer is thus accelerated but the numerical results closely match the analytical ones. The last part is dedicated to test cases. Two mains cases are studied The first one is the interaction between a vortex-ring and a no-slip wall with different initial angles relative to the ring axis. When the vortex-ring approaches the no-slip wall, a boundary layer develops. After some time, the boundary layer separation occurs and the vorticity wraps the vortex ring. It generates a secondary vortex-ring that impacts the dynamic of the primary one. Omega-loops instabilities are generated, which causes the destruction of the vortex-ring core. The second is a turbulent channel flow at low Reynolds number. The results are compared to the ones obtained by Moser and Lee. They match each other very closely. Some differences are observed at the middle of the channel, due to the shorter length of the computational domain used with VPM than the one used by Moser and Lee. Finally, an appendix shows nice results for a turbulent boundary layer development. The results are a little bit under resolved but the thicknesses, the Reynolds numbers and some velocity profiles are shown and discussed.