Solution of the 2 D Incompressible Navier-Stokes Equations on a Moving Voronoi Mesh

An incompressible 2D Navier-Stokes solver was implemented on a moving Voronoi mesh grid. The implementation of general Voronoi polygons for computational fluid dynamics (CFD) algorithms has recently gained interest due to the desire to simulate flows with complex physical phenomena. The solver has been implemented on a periodic domain and has been verified using a viscous Taylor Green vortex, diffusion of a shear layer, and simulations of the development of KelvinHelmholtz instabilities. The control volumes (CVs) are advected with the local velocity field to utilize the advantages of a Lagrangian fluid dynamics formulation. Python and the associated scientific computing packages [3] were used for coding. The algorithm is shown to be first order convergent in space and time.