Abstract
A full upwind finite element scheme based on the Petrov-Galerkin formulation is presented for accurate solutions of high Reynolds number flows, and then a simplified finite scheme with third-order upwinding is developed in order to obtain a practical algorithm for numerical simulation, because structures of the full upwind finite element scheme are very complicated. Numerical dissipation added in the proposed upwind scheme is represented by high-order derivatives of flow velocities and pressure. Computational results for the subcritical and the supercritical Reynolds number flows around a circular cylinder and for flows around twin circular cylinders are shown to illustrate the effectiveness and robustness of the simplified upwind finite element scheme.
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