Abstract

Upwind—Least Square Finite Difference (LSFD-U) is a generalized finite difference method capable of operating on an arbitrary distribution of points. The method is known to work well on an isotropic distribution of points typically needed for inviscid computations. However, on highly anisotrpoic distribution of points as encountered in the viscous padding region associated with the RANS computations, (i.e. high aspect ratio volumes in finite volumes parlance) these methods tend to fail because of the ill-conditioning of the associated geometric matrix. This necessitates the use of rotated coordinates for update in this region. Yet another difficulty associated with such point distributions is the sharp turning the grid lines experience at certain locations (for example, near the trailing edge of airfoil). These are identified as regions of grid folding. The work proposes two different ways for mitigating this difficulty. In the first approach points are added around points identified with grid folding and the second approach simply involves placing the fictitious interface close to these points, in contrast with the earlier convention of placing these fictitious interfaces mid-way along a ray connecting two points under consideration. Both these methods attempt to recover an isotropic distribution of points in the region of grid folding. The method is successfully demonstrated for simulating 2D high lift flows.

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