Finite element implementation of two-equation and algebraic stress turbulence models for steady incompressible flows

The main purpose of this paper is to describe a finite element formulation for solving the equations for k and e of the classical k–e turbulence model, or any other two-equation model. The finite element discretization is based on the SUPG method together with a discontinuity capturing technique to deal with sharp internal and boundary layers. The iterative strategy consists of several nested loops, the outermost being the linearization of the Navier–Stokes equations. The basic k–e model is used for the implementation of an algebraic stress model that is able to account for the effects of rotation. Some numerical examples are presented in order to show the performance of the proposed scheme for simulating directly steady flows, without the need of reaching the steady state through a transient evolution. Copyright © 1999 John Wiley & Sons, Ltd.

[1]  Claes Johnson,et al.  On the convergence of a finite element method for a nonlinear hyperbolic conservation law , 1987 .

[2]  Miguel Cervera,et al.  The intrinsic time for the streamline upwind/Petrov-Galerkin formulation using quadratic elements , 1992 .

[3]  T. Utnes.  Two-equation (k, ε) turbulence computations by the use of a finite element model , 1988 .

[4]  R. M. Smith.  A practical method of two‐equation turbulence modelling using finite elements , 1984 .

[5]  F. Shakib.  Finite element analysis of the compressible Euler and Navier-Stokes equations , 1989 .

[6]  M. Wolfshtein,et al.  Turbulent time scale for turbulent-flow calculations , 1986 .

[7]  H.E.A. van den Akker,et al.  Single-phase flow in stirred reactors , 1994 .

[8]  J. L. Fleming,et al.  An experimental study of a turbulent wing-body junction and wake flow , 1992 .

[9]  Ramon Codina,et al.  A discontinuity-capturing crosswind-dissipation for the finite element solution of the convection-diffusion equation , 1993 .

[10]  Ramon Codina,et al.  An iterative penalty method for the finite element solution of the stationary Navier-Stokes equations , 1993 .

[11]  Charles G. Speziale,et al.  ANALYTICAL METHODS FOR THE DEVELOPMENT OF REYNOLDS-STRESS CLOSURES IN TURBULENCE , 1990 .

[12]  T. Gatski,et al.  On explicit algebraic stress models for complex turbulent flows , 1992, Journal of Fluid Mechanics.

[13]  Miguel Cervera,et al.  On the computational efficiency and implementation of block-iterative algorithms for nonlinear coupled Problems , 1996 .

[14]  O. Pironneau,et al.  Analysis of the K-epsilon turbulence model , 1994 .

[15]  A. Galeão,et al.  A consistent approximate upwind Petrov—Galerkin method for convection-dominated problems , 1988 .

[16]  James P. Johnston,et al.  Investigation of a Reattaching Turbulent Shear Layer: Flow Over a Backward-Facing Step , 1980 .

[17]  D. Wilcox.  Reassessment of the scale-determining equation for advanced turbulence models , 1988 .

[18]  M. A. Cavaliere,et al.  An iterative (k‐L)‐predictor/ε‐corrector algorithm for solving (k‐ε) turbulent models , 1997 .

[19]  R. Codina,et al.  A discontinunity capturing crosswind-dissipation for the finite element solution of the convection-diffusion equation , 1993 .

[20]  I. Dekeyser,et al.  Finite element computation of a turbulent flow over a two‐dimensional backward‐facing step , 1987 .

[21]  Michel Fortin,et al.  Mixed and Hybrid Finite Element Methods , 2011, Springer Series in Computational Mathematics.

[22]  Ali Cemal Benim,et al.  Investigation into the finite element analysis of confined turbulent flows using a κ-ε model of turbulence☆ , 1985 .

[23]  D. Wilcox.  Turbulence modeling for CFD , 1993 .

[24]  P. Bradshaw,et al.  Turbulence Models and Their Application in Hydraulics. By W. RODI. International Association for Hydraulic Research, Delft, 1980. Paperback US $15. , 1983, Journal of Fluid Mechanics.

[25]  P. Bradshaw,et al.  Turbulence Models and Their Application in Hydraulics. By W. RODI. International Association for Hydraulic Research, Delft, 1980. Paperback US $15. , 1983, Journal of Fluid Mechanics.

[26]  T. Hughes,et al.  Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations , 1990 .

[27]  Marc Jaeger,et al.  An extended κ-ε finite element model , 1992 .

[28]  W. Rodi,et al.  ERCOFTAC Workshop on Data Bases and Testing of Calculation Methods for Turbulent Flows , 1995 .