Hybrid vortex/magnet methods for flow over a solid boundary

¹ Mathematics Department Napier University 219 Colinton Road Edinburgh, EH14 1DJ, Scotland
² Department of Mathematics University of California Berkeley, CA94720, USA

Abstract

Boundary conditions, in particular no-slip boundary conditions, are usually imposed in vortex methods through the creation of vorticity. In three dimensions, this is typically done by creating vortex "blobs" or "segments". However, with these computational elements, one compromises accuracy by losing the divergence-free nature of the vorticity field. Furthermore, these methods preclude the use of hairpin removal strategies for simplifying the calculation. We explore remedies for this problem through the use of discrete elements of fluid impulse (also known as "magnets"). In particular, two strategies for evolving impulse from a boundary, consistent with the no-slip condition, are proposed; they correspond to two choices of gauge. Sheet-like elements are created at walls to carry this impulse; as these elements diffuse away from the wall into the flow interior they are transformed into vortex loops of equal impulse. In this way hybrid vortex algorithms are determined for three-dimensional incompressible bounded flow. These ideas are illustrated by numerical experiment with high Reynolds number flow past a sphere.