Von Neumann Turbulent Transport Model

TL;DR

This paper introduces a simple, grid-dependent model for turbulent transport coefficients in multi-phase hydrodynamics, inspired by von Neumann artificial viscosity, which activates based on flow stability criteria.

Contribution

It presents a novel analogy-based model for subgrid turbulent diffusivity and viscosity that explicitly incorporates grid size and flow stability conditions.

Findings

Coefficients depend on grid size and are zero in non-turbulent flows.

Model adapts to flow stability, activating turbulence modeling when instability criteria are met.

Provides a practical approach for subgrid turbulence in numerical simulations.

Abstract

I propose a simple model, based on an analogy to von Neumann artificial viscosity, of turbulent diffusion, heat diffusion and viscosity coefficients for use in modeling subgrid turbulent diffusivity in multi-phase numerical hydrodynamics and, more generally, in subgrid turbulent viscosity and thermal transport. In analogy to the von Neumann artificial viscosity, these coefficients explicitly contain the grid size and do not attempt a quantitative model of the unresolved turbulence. In order to address the problem that it is often not known a priori when and where a flow will become turbulent, the coefficients are set to zero when the flow is not expected to be turbulent on the basis of a Richardson/Rayleigh-Taylor stability criterion, in analogy to von Neumann's setting of artificial viscosity to zero in expanding flows.