We discuss three methods for the simulation of turbulent fluids. The issue we address is not the important issue of numerical algorithms, but the even more basic question of the equations to be solved, otherwise known as the turbulence model. These equations are not simply the Navier-Stokes equations, but have extra, turbulence related terms, related to turbulent viscosity, turbulent diffusion and turbulent thermal conductivity. The extra terms are not “standard textbook” physics, but are hypothesized based on physical reasoning. Here we are concerned with these extra terms.
The many models, divided into broad classes, differ greatly in
Dependence on data
Complexity
Purpose and usage
For this reason, each of the classes of models has its own rationale and domain of usage.
We survey the landscape of turbulence models.
Given a turbulence model, we ask: what is the nature of convergence that a numerical algorithm should strive for? The answer to this question lies in an existence theory for the Euler equation based on the Kolmogorov 1941 turbulent scaling law, taken as a hypothesis (joint work with G-Q Chen).