Efficient incompressible flow calculations using PQ2Q1 element

Implementation of an equal-order-interpolation velocity-pressure element pair is presented for the 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 subdivisions of the pressure element. This pair satisfies the so-called '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 and efficiency of the element compared to a regular bilinear velocity-pressure (Q1Q1) element pair. Computational results presented show that the pQ2Q1 element solutions require less memory and CPU time compared to Q1Q1 element solutions, for at least the same accuracy.