Simulation of two-dimensional flow around an elliptical cylinder at high Reynolds numbers

Abstract

The modified viscous vortex domains method is used for direct numerical simulation of two-dimensional flow around an elliptical cylinder at the Reynolds number up to Re = 106. The modified method is based on the use of a conformal mapping from the outer region of an ellipse to the outer region of a circle. Transformed Navier–Stokes equations under an arbitrary conformal mapping are derived. These equations are solved in the mapped plane. An efficient algorithm for calculating boundary elements, previously developed to calculate the flow around a circular cylinder, is applied. The application of this algorithm makes it possible to reduce the calculation time by orders of magnitude and significantly expands the possibilities of flow simulation at high values of the Reynolds number. The method developed in this work can be implemented in other vortex methods.