Abstract

Our concept for numerical schemes is based on two relations: 1) a polynomial and the derivatives, and 2) a polynomial and the integrations. The Taylor series expansion of a function q about a certain point and the Lagrangian interpolation formula are utilized to construct the upwind scheme on a physical space. Three results in two dimensions are shown: a motion of viscous vortex with a uniform background flow, a driven cavity flow, and a flow past a circular cylinder. The method presented produces smooth and realistic results for computations with stretched meshes

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