Introduction

In Chapter 4e, a computational method based on vorticity confinement (VC) is described that has been designed to capture thin vortical regions in high-Reynolds-number incompressible flows. The principal objective of the method is to capture the essential features of these small-scale vortical structures and model them with a very efficient difference method directly on an Eulerian computational grid. Essentially, the small scales are modeled as nonlinear solitary waves that “live” on the lattice indefinitely. The method allows convecting structures to be modeled over as few as two grid cells with no numerical spreading as they convect indefinitely over long distances, with no special logic required for merging or reconnection. It can be used to provide very efficient models of attached and separating boundary layers, vortex sheets, and filaments. Further, the method easily allows boundaries with no-slip conditions to be treated as “immersed” surfaces in uniform, nonconforming grids, with no requirements for complex logic involving “cut” cells.

There are close analogies between VC and well-known shock- and contact-discontinuity-capturing methodologies. These were discussed in Chapter 4e to explain the basic ideas behind VC, since it is somewhat different than conventional computational fluid dynamics (CFD) methods. Some of the possibilities that VC offers toward the very efficient computation of turbulent flows, which can be considered to be in the implicit large eddy simulation (ILES) spirit, were explored. These stem from the ability of VC to act as a negative dissipation at scales just above a grid cell, but that saturates and does not lead to divergence.