On the performance of high aspect ratio elements for incompressible flows

Abstract

A systematic study of the effect of high aspect ratio elements using equal-order-interpolation velocity-pressure elements for computation of incompressible flows is conducted. Both, quadrilateral and triangular elements utilizing, bilinear (Q1Q1) and linear (P1P1) interpolation functions, respectively, are considered. Stabilized finite-element formulations are employed to solve the incompressible Navier-Stokes equations in the primitive variables. The element length, h, plays an important role in the calculation of stabilizing coefficients in the formulation. Three definitions of h are utilized. These are based on the maximum edge length, minimum edge length of an element and the element length along the streamwise direction. Performance of the implementations is evaluated for both, steady and unsteady flows. Numerical experiments are conducted for flow past a circular cylinder at Reynolds numbers 10 and 100. While in the former case the flow is steady, the latter one is associated with temporally periodic vortex shedding. It is observed that for the Re=10 flow all definitions of h produce acceptable solutions even with elements that have very high aspect ratios. In the case of Re=100 flow, again, all definitions of h work well for elements with reasonable/low aspect ratios. However, for large aspect ratio elements it is only the definition based on the minimum edge length of an element that results in acceptable solution. It is also observed that the effect of high aspect ratio is felt more by the P1P1 element as compared to the Q1Q1 element.