On the performance of high aspect ratio elements for incompressible flows

A systematic study of the effect of high aspect ratio elements using equal- order-interpolation velocity-pressure elements for computation of incompres sible Rows is conducted. Both, quadrilateral and triangular elements utiliz ing, bilinear (Q1Q1) and linear (P1P1) interpolation functions, respectivel y, are considered. Stabilized finite-element formulations are employed to s olve the incompressible Navier-Stokes equations in the primitive variables. The element length, h, plays an important role in the calculation of stabi lizing coefficients in the formulation. Three definitions of It are utilize d. These are based on the maximum edge length, minimum edge length of an el ement and the element length along the streamwise direction. Performance of the implementations is evaluated for both, steady and unsteady flows. Nume rical experiments are conducted for flow past a circular cylinder at Reynol ds numbers 10 and 100. While in the former case the flow is steady, the lat ter one is associated with temporally periodic vortex shedding. It is obser ved that for the Re = 10 flow all definitions of h produce acceptable solut ions even with elements that have very high aspect ratios. In the case of R e = 100 flow, again, all definitions of h work well for elements with reaso nable/low aspect ratios. However, for large aspect ratio elements it is onl y the definition based on the minimum edge length of an element that result s in acceptable solution. It is also observed that the effect of high aspec t ratio is felt more by the P1P1 element as compared to the Q1Q1 element. ( C) 2000 Elsevier Science S.A. All rights reserved.