- Epstein, Ronald J. and Bliss, Donald B., Free vortex calculations using analytical/numerical matching with solution pyramiding,
AIAA Journal, vol. 33 no. 5
pp. 894 - 903 .
(last updated on 2007/04/09)
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 capitalizes on the disparity of characteristic length scales 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, and 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 and 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 and vortex ring motion and interactions, this method was found to be relatively easy to implement and exhibited reductions in computational time from a factor of three to more than an order of magnitude.
Calculations;Numerical methods;Computational fluid dynamics;Three dimensional;Vectors;Lagrange multipliers;Differential equations;