Large eddy simulation of three-dimensional turbulent flows by the finite element method

The main objectives of this work are the formulation, implementation and applications of a numerical algorithm to simulate turbulent, incompressible, isothermal flows. The transient three-dimensional flow is analyzed using an explicit Taylor-Galerkin scheme and the finite element method with hexahedrical eight-node element. Turbulence is simulated using Large Eddy Simulation. For sub-grid scales two models were implemented, the classical Smagorinsky's model and the dynamic eddy viscosity model. For the second filtration, which is necessary in the dynamic model, a new method was developed based on independent finite elements that involve each node in the original mesh. The implemented scheme is efficient and good results with low additional computational cost were obtained. Results for two classical problems, the driven cavity and the backward facing step are presented. Comments about the model applicability for flows with high Reynolds numbers are also presented.

[1]  Mutsuto Kawahara,et al.  A finite element method for high Reynolds number viscous fluid flow using two step explicit scheme , 1983 .

[2]  W. Rodi,et al.  Large-Eddy Simulation of Turbulent Flow through a Straight Square Duct and a 180° Bend , 1994 .

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

[4]  J. Lumley,et al.  A First Course in Turbulence , 1972 .

[5]  J. Reddy,et al.  The Finite Element Method in Heat Transfer and Fluid Dynamics , 1994 .

[6]  L. Franca,et al.  Stabilized finite element methods. II: The incompressible Navier-Stokes equations , 1992 .

[7]  J. Koseff,et al.  A dynamic mixed subgrid‐scale model and its application to turbulent recirculating flows , 1993 .

[8]  S. Menon,et al.  AN UNSTEADY INCOMPRESSIBLE NAVIER-STOKES SOLVER FOR LARGE EDDY SIMULATION OF TURBULENT FLOWS , 1999 .

[9]  R. Denaro.  TOWARDS A NEW MODEL‐FREE SIMULATION OF HIGH‐REYNOLDS‐FLOWS: LOCAL AVERAGE DIRECT NUMERICAL SIMULATION , 1996 .

[10]  P. Moin,et al.  Numerical Simulation of Turbulent Flows , 1984 .

[11]  B. Armaly,et al.  Experimental and theoretical investigation of backward-facing step flow , 1983, Journal of Fluid Mechanics.

[12]  H. Schlichting.  Boundary Layer Theory , 1955 .

[13]  Toshio Kobayashi,et al.  Development of a Filtering Operation for Dynamic SGS Model Using the Finite Element Method , 1997 .

[14]  J. Smagorinsky,et al.  GENERAL CIRCULATION EXPERIMENTS WITH THE PRIMITIVE EQUATIONS , 1963 .

[15]  A. J. Baker,et al.  Numerical simulations of laminar flow over a 3D backward‐facing step , 1997 .

[16]  Joel H. Ferziger,et al.  Simulation of complex turbulent flows: recent advances and prospects in wind engineering , 1993 .

[17]  J. Z. Zhu,et al.  The finite element method , 1977 .

[18]  D. Lilly,et al.  A proposed modification of the Germano subgrid‐scale closure method , 1992 .

[19]  P. Moin,et al.  A dynamic subgrid‐scale eddy viscosity model , 1990 .

[20]  Marcel Lesieur,et al.  A numerical investigation of the coherent vortices in turbulence behind a backward-facing step , 1993, Journal of Fluid Mechanics.

[21]  J. Koseff,et al.  Reynolds number and end‐wall effects on a lid‐driven cavity flow , 1989 .

[22]  Robert L. Street,et al.  Mathematical Description of Turbulent Flows , 1982 .

[23]  George Em Karniadakis,et al.  Onset of three-dimensionality, equilibria, and early transition in flow over a backward-facing step , 1991, Journal of Fluid Mechanics.

[24]  L. Franca,et al.  Stabilized Finite Element Methods , 1993 .

[25]  J. Donea.  A Taylor–Galerkin method for convective transport problems , 1983 .

[26]  F. White.  Viscous Fluid Flow , 1974 .