Phd in MATHEMATICS

Thesis title: 2d viscous flow studied using vortex particle methods

Vortex particle methods are alternative methods to Eulerian approaches for the solution of the incompressible Navier-Stokes equations in vorticity-velocity variables. They are characterized by the inherent ability to adapt to the flow due to their Lagrangian formulation for the advection and additionally by the decoupling of the pressure from the momentum equation. In this work, we study these methods using the Lagrangian vortex particle method Diffused Vortex Hydrodynamics that uses the operator splitting in time of Chorin. Numerical results are obtained for problems containing solid boundaries in the domain for different test cases. We compare the results with a finite volume solver that discretizes the velocity-pressure formulation of Navier-Stokes and uses artificial compressibility to evolve the solution in time, also introduced by Chorin. The comparison is obtained based on local and global derived quantities. Finally, an application of the method to a physical study is presented regarding the flow past an elliptical cylinder.