Free vortex calculations using analytical/numerical matching with solution pyramiding

Abstract

The motion of a free vortex system is predicted using a novel method called analytical/numerical matching (ANM). Analytical/numerical matching is a hybrid mathematical and numerical technique that results in a new problem formulation with high accuracy and increased computational efficiency. The approach capitalizer on the disparity of characteristic length scaler that occur in many fluid dynamics problems. Accordingly, many problems can be decomposed into two distinct problems involving a local high-resolution near field, often solvable analytically, end a global, low-resolution far field, solved numerically. The ANM technique breaks the free vortex problem into these local and global problems each of which are easier end more efficient to solve than the traditional problem formulation. In addition, the ANM decomposition can be repeated to form a hierarchy of nested problems of increasing resolution using a method called pyramiding. The ANM method with pyramiding, called ANM/P, is studied to assess its accuracy and computational efficiency for two-dimensional and three-dimensional vortex dynamics problems. In calculations of vortex sheet rollup end vortex ring motion and interactions, this method war found to be relatively easy to implement end exhibited reductions in computational time from a factor of three to more than an order of magnitude