A Simple Redistribution Vortex Method (with Accurate Body Forces)

TL;DR

This paper introduces a simple and efficient vortex redistribution scheme for viscous flow simulations that improves accuracy of surface force calculations without requiring vortex core overlap.

Contribution

It presents a novel circulation redistribution method that transfers circulation to fixed nodes, enabling high-resolution and accurate force estimation in vortex methods.

Findings

The scheme is simple and explicit, making it computationally efficient.

It produces smooth, accurate surface force estimates.

Demonstrated high-resolution results on test problems.

Abstract

A circulation redistribution scheme for viscous flow is presented. Unlike other redistribution methods, it operates by transferring the circulation to a set of fixed nodes rather than neighbouring vortex elements. A new distribution of vortex elements can then be constructed from the circulation on the nodes. The solution to the redistribution problem can be written explicitly as a set of algebraic formulae, producing a method which is simple and efficient. The scheme works with the circulation contained in the vortex elements only, and does not require overlap of vortex cores. With a body fitted redistribution mesh, smooth and accurate estimates of the pointwise surface forces can be obtained. The ability of the scheme to produce high resolution solution is demonstrated using a series of test problems.