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.