Efficient incompressible flow calculations using PQ2Q1 element

Abstract

We present implementation of an equal-order-interpolation velocity-pressure element pair for finite element solution of incompressible viscous flows. A fractional-step method is employed for temporal discretization. The element pair, also called a pseudo-biquadratic velocity/bilinear pressure element (pQ2Q1), consists of a bilinear pressure element and bilinear velocity elements defined on subdivisons of the pressure element. This pair satisfies Ladyzhenskaya-Babuska-Brezzi condition. Considerable savings in computational cost are achieved due to the reduced number of elements for pressure. A modification of the element is realized for a better representation of curved surfaces. Two test cases, namely the lid-driven cavity flow and impulsively started circular cylinder in cross-flow, are used to assess the accuracy of the method.