A Tri-Tree multigrid recoarsement algorithm for the finite element formulation of the Navier-Stokes equations Original Research Article

present paper local recoarsements of finite element grids for solving the Navier-Stokes equations are investigated. The recoarsement algorithm is based on the hierarchic Tri-Tree multigrid generation algorithm and computes a local Tri-Tree Element Reynolds number. Previous investigations show that the Element Reynolds number is critical for convergence of the linear CGSTAB equation solver. A necessary condition for convergence is found to be that the Element Reynolds number is less than 10. The Tri-Tree multigrid solution algorithm starts by solving the equations for a low Reynolds number for a coarse grid. Solutions for higher Reynolds numbers are obtained by gradually increasing the velocity boundary conditions while refining the grid correspondingly to satisfy the Element Reynolds criterion. As the global Reynolds number is increasing, the non-linear convection moves in space. The recoarsement algorithm is then making the grid coarser at locations where the previous fine grid resolution is no longer required.