MAST-RT0 solution of the incompressible Navier–Stokes equations in 3D complex domains

Abstract

A new numerical methodology to solve the 3D Navier-Stokes equations for incompressible fluids within complex boundaries and unstructured body-fitted tetrahedral mesh is presented and validated with three literature and one real-case tests. We apply a fractional time step procedure where a predictor and a corrector problem are sequentially solved. The predictor step is solved applying the MAST (Marching in Space and Time) procedure, which explicitly handles the non-linear terms in the momentum equations, allowing numerical stability for Courant number greater than one. Correction steps are solved by a Mixed Hybrid Finite Elements discretization that assumes positive distances among tetrahedrons circumcentres. In 3D problems, non-Delaunay meshes are provided by most of the mesh generators. To maintain good matrix properties for non-Delaunay meshes, a continuity equation is integrated over each tetrahedron, but the momentum equations are integrated over clusters of tetrahedrons, such that each external face shared by two clusters belongs to two tetrahedrons whose circumcentres have positive distance. A numerical procedure is proposed to compute the velocities inside clusters with more than one tetrahedron. Model preserves mass balance at the machine error and there is no need to compute pressure at each time iteration, but only at target simulation times.

Keywords

• navier–stokes equations
• 3d numerical model
• eulerian method
• unstructured tetrahedral mesh
• predictor–corrector scheme
• mixed hybrid finite element