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This paper proposes a numerical method for computing the flows at high Reynolds number (Re). A modified fractional step (FS) finite element method (FEM) is based upon the velocity correction method (VCM) and uses two concepts to conduct intermediate velocity. The first is the streamline method, which provides an accurate multidimensional generalization, and the second is the balancing tensor diffusivity (BTD), which is used as the artificial diffusion for the stabilization techniques. The accuracy of this method for the advection-diffusion equation is demonstrated for the rotating cone problem. The unsteady incompressible viscous flows, such as square cavity flow at Re≤10000 and flow past a cylinder at Re≤2000, are simulated without any numerical instability.

A Modified Streamline Fractional Step Finite Element Method for Solving Unsteady Incompressible Viscous Flow