A Lagrangian fractional step method for the incompressible Navier-Stokes equations on a periodic domain (Q1111850)

A new Lagrangian method is presented for solving the two-dimensional incompressible Navier-Stokes equations in primitive variables on a periodic domain. A collection of N moving points (fluid markers) serve as a grid. The associated Voronoi diagram is used for the construction of the finite-difference operators corresponding to the divergence, gradient and Laplacian. A Lagrangian version of Chorin's projection method is considered for the time discretization. This requires the solution of a Poisson equation for the pressure and a Helmholtz equation for each velocity component at each time step. A two-grid method is proposed for solving the discretized equations. The second grid involved is not obtained by coarsening but by regularization: A regular grid of roughly N points is introduced. On this grid the equations are solved exactly by using Fast Fourier Transform. Numerical results are reported for four test problems.