Abstract
Numerical simulation of turbulent flows over different aerofoil configurations are presented in this paper. The incompressible fluid flow is described by the time-dependent incompressible Navier–Stokes equations. Further, a finite element variational multiscale method is used to simulate the turbulent flows. Computation over a cylinder and different variants of aerofoils are presented. The obtained numerical results demonstrate the capabilities of variational multiscale methods.
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References
Davidson, P.A.: Turbulence: An Introduction for Scientists and Engineers. Oxford University Press, Oxford (2004)
Pope, S.B.: Turbulent Flows. Cambridge University Press, Cambridge (2000)
Chen, H.C., Patel, V.C., Ju, S.: Solutions of Reynolds-averaged Navier–Stokes equations for three-dimensional incompressible flows. J. Comput. Phys. 88, 305–336 (1990)
Fischer, P., Iliescu, T.: Large eddy simulation of turbulent channel flows by the rational les model. Phys. Fluids 15, 3036–3047 (2003)
Guermond, J.L., Oden, J.T., Prudhomme, S.: Mathematical perspectives on large eddy simulation models for turbulent flows. J. Math. Fluid Mech. 6, 194–248 (2004)
Rogallo, R.S., Moin, P.: Numerical simulation of turbulent flows. Ann. Rev. Fluid Mech 16, 99–137 (1984)
Sagaut, P.: Large Eddy Simulation for Incompressible Flows, 2nd edn. Springer, Berlin (2002)
Hughes, T.J.R.: Multiscale phenomena: green’s functions, the dirichlet to neumann formulation, subgrid scale models, bubbles and origins of stabilized methods. Comput. Methods Appl. Mech. Eng. 127, 387–401 (1995)
Hughes, T.J.R., Feijoo, G.R., Mazzei, L., Quincy, J.B.: The variational multiscale method—a paradigm for computational mechanics. Comput. Methods Appl. Mech. Eng. 166, 3–24 (1998)
Collis, S.S.: Monitoring unresolved scales in multiscale turbulence modelling. Phys. Fluids 13(6), 1800–1806 (2001)
Gamnitizer, P., Gravemeier, V., Wall, W.A.: Advances in variational multiscale methods for turbulent flows. In: de Borst, R., Ramm, E. (eds.) Multiscale Methods in Computational Mechanics. Lecture Notes in Applied and Computational Mechanics, pp. 39–52. Springer, Berlin (2011)
Gravemeier, V.: The variational multiscale methods for laminar and turbulent incompressible flows. Phd thesis, Institute of Structural Mechanics, University of Stuttgart (2003)
John, V.: On large eddy simulation and variational multiscale methods in the numerical simulation of turbulent incompressible flows. Appl. Math. 51(4), 321–353 (2006)
John, V., Kaya, S., Layton, W.J.: A two-level variational multiscale method for convection-dominated convection diffusion equations. Comput. Methods Appl. Mech. Eng. 195, 4594–4603 (2006)
John, V., Layton, W.J.: Subgrid scale eddy viscosity models and variational multiscale methods. Technical report TR-MATH 03–05. University of Pittsburgh (2003)
John, V., Kaya, S.: Finite element error analysis of a variational multiscale method for Navier–Stokes equations. Adv. Comp. Math. 28, 43–61 (2008)
John, V.: Large Eddy Simulation of Turbulent Incompressible Flows. Analytical and Numerical Results for a Class of LES Models. Lecture Notes in Computational Science and Engineering. Springer, Berlin (2004)
Gamnitizer, P., Gravemeier, V., Wall, W.A.: Time-dependent subgrid scales in residual-based large eddy simulation. Comput. Methods Appl. Mech. Eng. 199, 819–827 (2010)
Hughes, T.J.R., Mazzei, L., Jensen, K.E.: Large eddy simulation and variational multiscale methods. Comput. Vis. Sci. 3, 47–59 (2000)
Hughes, T.J.R., Oberai, A.A., Mazzei, L.: Large eddy simulation of turbulent channel flows by the variational multiscale method. Phys. Fluids 13(6), 1784–1799 (2001)
Gravemeier, V., Wall, W.A., Ramm, E.: A three level finite element method for instationary incompressible Navier–Stokes equations. Comput. Methods Appl. Mech. Eng. 193, 1323–1366 (2004)
Gravemeier, V., Wall, W.A., Ramm, E.: Large eddy simulation of turbulent incompressible flows by a three-level finite element method. Int. J. Numer. Methods Fluids 48, 1067–1099 (2005)
Masud, A., Calderer, R.: A variational multiscale method for incompressible turbulent flows: bubble functions and fine scale fields. Comput. Methods Appl. Mech. Eng. 200, 2577–2593 (2011)
John, V., Kaya, S.: A finite element variational multiscale method for the Navier–Stokes equation. SIAM J. Sci. Comput. 26(5), 1485–1503 (2005)
Gravemeier, V.: Scale-seperating operators for variational multiscale large eddy simulation of turbulent flows. J. Comput. Phys. 212, 400–435 (2006)
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Pal, B., Ganesan, S. A finite element variational multiscale method for computations of turbulent flow over an aerofoil. Int J Adv Eng Sci Appl Math 7, 14–24 (2015). https://doi.org/10.1007/s12572-015-0126-1
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DOI: https://doi.org/10.1007/s12572-015-0126-1