A Petrov-Galerkin formulation for incompressible flow at high Reynolds number

A mixed finite element method was applied to solve a set of elliptic partial differential equations which corresponds to steady-state incompressible laminar how. To obtain stable solutions at high Reynolds numbers, the Petrov-Galerkin finite element method was used to discretize the advective flux terms with a biquadratic velocity-bilinear pressure element. A priori knowledge of the M-matrix has been used as an underlying guide to enhance the solution stability. The main impetus and effort involve designing a test space of an exponential type. The test cases considered and the results obtained show that the proposed Petrov-Galerkin method is highly reliable and applicable to a wide range of flow conditions.