Residual-based variational multiscale methods for laminar, transitional and turbulent variable-density flow at low Mach number

International Journal for Numerical Methods in Fluids

Volumn 65, Issue 10, 2011, Pages 1260-1278

  Gravemeier, Volker ^a   Wall, Wolfgang A ^a  

^a TECHNICAL UNIVERSITY OF MUNICH   (Germany)

Author keywords

Finite element method; Large eddy simulation; Low Mach number; Turbulent flow; Variable density flow; Variational multiscale method

Indexed keywords

CONSERVATION EQUATIONS; DENSITY FLOW; FLOW TESTS; HIGH TEMPERATURE GRADIENT; LOW MACH NUMBERS; NUMERICAL EXAMPLE; REYNOLDS STRESS; STABILIZED FORMULATION; SUBGRID SCALE; TEST CASE; VARIABLE-DENSITY FLOW; VARIATIONAL MULTISCALE; VARIATIONAL MULTISCALE METHODS;

AERODYNAMICS; ATMOSPHERIC BOUNDARY LAYER; FINITE ELEMENT METHOD; LAMINAR FLOW; LARGE EDDY SIMULATION; MACH NUMBER; TURBULENT FLOW;

FLOW SIMULATION;

EID: 79952122675     PISSN: 02712091     EISSN: 10970363     Source Type: Journal    
DOI: 10.1002/fld.2242     Document Type: Article

References (50)

1. Poinsot T, Veynante D. Theoretical and Numerical Combustion (2nd edn). R.T. Edwards: Philadelphia, PA, 2005.
2. Majda A, Sethian J. The derivation and numerical solution of the equations for zero Mach number combustion. Combustion Science and Technology 1985; 42:185-205.
3. Sagaut P. Large Eddy Simulation for Incompressible Flows (3rd edn). Springer: Berlin, 2006.
4. Geurts BJ. Elements of Direct and Large Eddy Simulation. R.T. Edwards: Philadelphia, PA, 2004.
5. Wang WP, Pletcher RH. On the large-eddy simulation of a turbulent channel flow with significant heat transfer. Physics of Fluids 1996; 8:3354-3366.
6. Pierce C, Moin P. Progress-variable approach for large eddy simulation of turbulent combustion. Report TF80, Flow Physics and Computation Division, Department of Mechanical Engineering, Stanford University, 2001.
7. Lessani B, Paplexandris MV. Time-accurate calculation of variable density flows with strong temperature gradients and combustion. Journal of Computational Physics 2006; 212:218-246.
8. Wang P, Fröhlich J, Michelassi V, Rodi W. Large-eddy simulation of variable-density turbulent axisymmetric jets. International Journal of Heat and Fluid Flow 2008; 29:654-664.
9. Nicoud F. Conservative high-order finite difference schemes for low-Mach number flows. Journal of Computational Physics 2000; 158:71-97.
10. Desjardins O, Blanquart G, Balarac G, Pitsch H. High order conservative finite difference scheme for variable density low Mach number turbulent flows. Journal of Computational Physics 2008; 227:7125-7159.
11. Codina R. Comparison of some finite element methods for solving the diffusion-convection-reaction equation. Computer Methods in Applied Mechanics and Engineering 1998; 156:185-210.
12. Hughes TJR, Scovazzi G, Franca LP. Multiscale and stabilized methods. In Encyclopedia of Computational Mechanics, Stein E, de Borst R, Hughes TJR (eds). Wiley: Chichester, 2004.
13. Braack M, Burman E, John V, Lube G. Stabilized finite element methods for the generalized Oseen problem. Computer Methods in Applied Mechanics and Engineering 2007; 196:853-866.
14. Hughes TJR, Scovazzi G, Tezduyar TE. Stabilized methods for compressible flows. Journal of Scientific Computing 2009; in press. Available from: http://dx.doi.org/10.1007/s10915-008-9233-5.
15. Brooks AN, Hughes TJR. Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations. Computer Methods in Applied Mechanics and Engineering 1982; 32:199-259.
16. Johnson C, Nävert U, Pitkäranta J. Finite element methods for linear hyperbolic problems. Computer Methods in Applied Mechanics and Engineering 1984; 45:285-312.
17. Hughes TJR, Franca LP, Balestra M. A new finite element formulation for computational fluid dynamics: V. Circumventing the Babuska-Brezzi condition: a stable Petrov-Galerkin formulation of the Stokes problem accommodating equal-order interpolation. Computer Methods in Applied Mechanics and Engineering 1986; 59:85-99.
18. Tezduyar TE, Mittal S, Ray SE, Shih R. Incompressible flow computations with stabilized bilinear and linear equal-order-interpolation velocity-pressure elements. Computer Methods in Applied Mechanics and Engineering 1992; 95:221-242.
19. Franca LP, Hughes TJR. Two classes of mixed finite element methods. Computer Methods in Applied Mechanics and Engineering 1988; 69:89-129.
20. De Mulder T. The role of bulk viscosity in stabilized finite element formulations for incompressible flow. Computer Methods in Applied Mechanics and Engineering 1998; 163:1-10.
21. Tezduyar TE, Osawa Y. Finite element stabilization parameters computed from element matrices and vectors. Computer Methods in Applied Mechanics and Engineering 2000; 190:411-430.
22. Bazilevs Y, Calo VM, Cottrell JA, Hughes TJR, Reali A, Scovazzi G. Variational multiscale residual-based turbulence modeling for large eddy simulation of incompressible flows. Computer Methods in Applied Mechanics and Engineering 2007; 197:173-201.
23. Hughes TJR, Feijoo GR, Mazzei L, Quincy J-B. The variational multiscale method-a paradigm for computational mechanics. Computer Methods in Applied Mechanics and Engineering 1998; 166:3-24.
24. Heuveline V. On higher-order mixed FEM for low Mach number flows: applications to a natural convection benchmark problem. International Journal for Numerical Methods in Fluids 2003; 41:1339-1356.
25. Martinez MJ, Gartling DK. A finite element method for low-speed compressible flows. Computer Methods in Applied Mechanics and Engineering 2004; 193:1959-1979.
26. Beccantini A, Studer E, Gournand S, Magnaud J-P, Kloczko T, Corre C, Kudriakov S. Numerical simulations of a transient injection flow at low Mach number regime. International Journal for Numerical Methods in Engineering 2008; 76:662-696.
27. Liu W, Makhviladze G. An implicit finite element solution of thermal flows at low Mach number. Journal of Computational Physics 2008; 227:2743-2757.
28. Principe J, Codina R. A stabilized finite element approximation of low speed thermally coupled flows. International Journal for Numerical Methods in Heat and Fluid Flow 2008; 18:835-867.
29. Braack M, Richter T. Stabilized finite elements for 3-D reactive flows. International Journal for Numerical Methods in Fluids 2006; 51:981-999.
30. Shadid JN, Tuminaro RS, Devine KD, Hennigan GL, Lin PT. Performance of fully coupled domain decomposition preconditioners for finite element transport/reaction simulations. Journal of Computational Physics 2005; 205:24-47.
31. Codina R, Blasco J. Analysis of a stabilized finite element approximation of the transient convection-diffusion-reaction equation using orthogonal subscales. Computing and Visualization in Science 2002; 4:167-174.
32. Codina R. Stabilized finite element approximation of transient incompressible flows using orthogonal subscales. Computer Methods in Applied Mechanics and Engineering 2002; 191:4295-4321.
33. Donea J, Huerta A. Finite Element Methods for Flow Problems. Wiley: Chichester, 2003.
34. Hughes TJR, Mazzei L, Jansen KE. Large eddy simulation and the variational multiscale method. Computing and Visualization in Science 2000; 3:47-59.
35. Gresho PM, Sani RL. Incompressible Flow and the Finite Element Method. Wiley: Chichester, 1998.
36. Akkerman I, Bazilevs Y, Calo VM, Hughes TJR, Hulshoff S. The role of continuity in residual-based variational multiscale modeling of turbulence. Computational Mechanics 2008; 41:371-378.
37. Gamnitzer P, Gravemeier V, Wall WA. Time-dependent subgrid scales in residual-based large eddy simulation of turbulent channel flow. Computer Methods in Applied Mechanics and Engineering 2009; in press. Available from: http://dx.doi.org/10.1016/j.cma.2009.07.009.
38. Hughes TJR, Wells GN. Conservation properties for the Galerkin and stabilised forms of the advection-diffusion and incompressible Navier-Stokes equations. Computer Methods in Applied Mechanics and Engineering 2005; 194:1141-1159.
39. Hughes TJR. The Finite Element Method: Linear Static and Dynamic Finite Element Analysis. Prentice-Hall: Englewood Cliffs, NJ, 1987.
40. Jansen KE, Whiting CH, Hulbert GM. A generalized-α method for integrating the filtered Navier-Stokes equations with a stabilized finite element method. Computer Methods in Applied Mechanics and Engineering 2000; 190:305-319.
41. Gravemeier V, Kronbichler M, Gee MW, Wall WA. An algebraic variational multiscale-multigrid method for large eddy simulation: generalized-α time integration, Fourier analysis and application to turbulent flow past a square-section cylinder. Computers and Fluids 2009; submitted for publication. Preprint.
42. Kirchartz KR, Oertel Jr H. Three-dimensional thermal cellular convection in rectangular boxes. Journal of Fluid Mechanics 1988; 192:249-286.
43. Tang LQ, Tsang TTH. Temporal, spatial and thermal features of 3-D Rayleigh-Benard convection by a least-squares finite element method. Computer Methods in Applied Mechanics and Engineering 1997; 140:201-219.
44. Prasad AK, Koseff JR. Reynolds number and end-wall effects on a lid-driven cavity flow. Physics of Fluids A 1989; 1:208-218.
45. Zang Y, Street RL, Koseff JR. A dynamic mixed subgrid-scale model and its application to turbulent recirculating flows. Physics of Fluids A 1993; 5:3186-3196.
46. Bouffanais R, Deville MO, Leriche E. Large-eddy simulation of the flow in a lid-driven cubical cavity. Physics of Fluids 2007; 19:055108-1-20.
47. Deshpande MD, George Milton S. Kolmogorov scales in a driven cavity flow. Fluid Dynamics Research 1998; 22:359-381.
48. Leriche E, Gavrilakis S. Direct numerical simulation of the flow in a lid-driven cubical cavity. Physics of Fluids 2000; 12:1363-1376.
49. Shankar PN, Deshpande MD. Fluid mechanics in the driven cavity. Annual Review of Fluid Mechanics 2000; 32:93-136.
50. Gravemeier V, Gee MW, Kronbichler M, Wall WA. An algebraic variational multiscale-multigrid method for large eddy simulation of turbulent flow. Computer Methods in Applied Mechanics and Engineering 2009; in press. Available from: http://dx.doi.org/10.1016/j.cma.2009.05.017.