A local solution adapted Tri-Tree multigrid generator and iterative equation solver for mixed finite element formulation of the Navier-Stokes equations Original Research Article

A multigrid algorithm for solving the Navier-Stokes equations is described. The generation of multigrids are based on the Tri-Tree unstructured grid generator. The Tri-Tree grid generation algorithm include local refinements. The spatial location of refinements are based on the solution calculated for the previous grid. The convection and diffusion terms are calculated for each Tri-Tree element and Tri-Tree elements with large convection-diffusion ratio refined. The finite element equation system is solved for subsequent locally refined grids. Local grid adaption to the solution correspond to linearization of the non-linear equation system. At each grid level, the Newton formulation of the finite element equation system is solved by an iterative, incomplete coupled node fill preconditioned equation solver. The solution adapted multigrid method is compared with the original Newton method for a single grid. At each grid level, the solution from the coarser grid is interpolated and projected to the new nodes on the finer grid and used as start vector. The finite element matrices are integrated analytically. The test problems considered are constricted tube flow and driven cavity flow.