Validation of a tetrahedral spectral element code for solving the Navier Stokes equation

The tetrahedral spectral element method is considered to solve the incompressible Navier-Stokes equations because it is capable to capture complex geometries and obtain highly accurate solutions. This method allows accuracy improvements both by decreasing the spatial discretization as well as increasing the expansion order. The method is presented here-in as a modification of an standard finite element code. Some recent improvement to the baseline spectral element method for the tetrahedron described in References 3 and 2 are presented. These improvements include: the continuity enforcement procedure avoiding the need to change the global assembly operation and the removal of the reference coordinate system from the elemental evaluations thus simplifying greatly the method. A study is performed on the Stokes and Navier-Stokes equations to validate the method and the resulting code. (author)