Abstract

This article is for those who have already a computer program for incompressible viscous transient flows and want to put a turbulence model into it. We discuss some of the implementation problems that can be encountered when the Finite Element Method is used on classical turbulence models except Reynolds stress tensor models. Particular attention is given to boundary conditions and to the stability of algorithms.

Introduction

Many scientists or engineers turn to turbulence modeling after having written a Navier-Stokes solver for laminar flows.

For them turbulence modeling is an external module into the computer program. Generally, the main ingredients to built a good Navier-Stokes solver are known; this includes tools like mixed approximations for the velocity u and pressure p to avoid checker board oscillations and also upwinding to damp high Reynolds number oscillations; however the problems that one may meet while implementing a turbulence model are not so well known because these models have not been studied much theoretically.

Judging from the literature [3] [11] [12] [15] [19] [22] the most commonly used turbulence models seem to be

• algebraic eddy viscosity models (zero equation models)

• k= ε models (two equations models)

• Reynolds stress models

All three start from a decomposition of u and p into a mean part and a fluctuating part u’. However oscillations are understood either as time oscillations or space oscillations or even variations due to changes in initial conditions. In any case, the decomposition u+u’ is applied to the Navier-Stokes equations.