A local predictive convection-diffusion refinement indicator for the Tri-Tree adapted finite element multigrid algorithm of the Navier-Stokes equations

Abstract

An element multigrid refinement algorithm based on the magnitude of the convection-diffusion ratio is investigated. The multigrid is generated by the Tri-Tree algorithm. The solution of the Navier-Stokes equations is first found for a low Reynolds number for a coarse grid. A directional Element Reynolds number is defined. The magnitude of the Element Reynolds number is investigated for Driven Cavity Flow for different grid resolutions, velocity boundary conditions and different cavity sizes. The results of these investigations show that CGSTAB iterative equation solver applied to the newton formulation of the Navier-Stokes equation, converges when the Element Reynolds number is below a limit. The Element Reynolds number limit is independent of element resolution, boundary velocity, and grid size. The Element Reynolds number is evaluated for all elements in the Tri-Tree grid and the Tri-Tree elements are refined recursively until the Element Reynolds number for all Tri-Tree elements has been reduced below a predefined limit.