BAIL 2006 Book of Abstracts - Institut für Numerische und ...

O. MIERKA, D. KUZMIN: On the implementation of turbulence models in incompressible
flow solvers based on a finite element discretization
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On the implementation of turbulence models in incompressible
flow solvers based on a finite element discretization
1. Introduction
O. Mierka and D. Kuzmin
Institute of Applied Mathematics (LS III), University of Dortmund
Vogelpothsweg 87, D-44227, Dortmund, Germany
omierka@math.uni-dortmund.de
kuzmin@math.uni-dortmund.de
The numerical implementation of turbulence models involves many algorithmic components
all of which may have a decisive influence on the quality of simulation results. In particular,
a positivity-preserving discretization of the troublesome convective terms and nonlinear
sources/sinks is an important prerequisite for the robustness of the numerical algorithm. This
paper presents a detailed numerical study of several eddy viscosity models implemented in the
open-source software package FeatFlow (http://www.featflow.de) using algebraic flux correction
to enforce the positivity constraint. The underlying finite element discretization and
iterative solution techniques are presented and relevant algorithmic details are revealed.
2. Algebraic flux correction schemes
The design of high-resolution finite element schemes for numerical simulation of turbulent incompressible
flows on the basis of eddy viscosity models is addressed. A robust positivity-preserving
algorithm is developed building on the algebraic flux correction paradigm for scalar transport
problems [1]. It is explained how to get rid of nonphysical oscillations in the vicinity of steep
gradients and to remove excessive artificial diffusion in regions where the solution is sufficiently
smooth. To this end, the discrete operators resulting from a standard Galerkin discretization
of convective terms are modified so as to enforce the desired matrix properies without violating
mass conservation.
3. Implementation of eddy viscosity models
The developed algebraic flux correction techniques are applied to high Reynolds number flows
that can be described by the incompressible Navier-Stokes equations coupled with an eddy
viscosity model of turbulence. A global Multilevel Pressure Schur Complement (discrete projection)
method is employed to enforce the incompressibility constraint at the discrete level [2].
The turbulent eddy viscosity is introduced in several different ways using
• the RANS approach as represented by various modifications of the k − ε model;
• Large Eddy Simulation (LES) with explicit and implicit subgrid scale modelling.
In particular, the advantages of Monotonically Integrated LES algorithms as compared to explicit
subgrid scale models of Smagorinsky type are explored. The implementation of the standard k−ε
model is based on a block-iterative algorithm featuring a positivity-preserving representation of
sink terms [2]. The main highlight of the present paper is a unified solution strategy for strongly
coupled PDE systems which result from 2D/3D finite element discretizations of RANS and
LES models on unstructured meshes. Special emphasis is laid on the near wall treatment and
Speaker: MIERKA, O. 118 BAIL 2006
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