Adaptive large eddy simulation with moving grids
Tóm tắt
The paper presents adaptive mesh moving methods for large eddy simulation (LES) of turbulent flows. With this approach, a given number of grid points is redistributed with respect to an appropriately selected criterion. The Arbitrary Lagrangian–Eulerian formulation is applied to solve the governing equation on moving grids employing a collocated finite volume formulation. A dynamic moving mesh partial differential equation based on a variational principle is solved for the corner points of the grid by means of a dedicated solver. Adaptation is performed in a statistical sense so that statistical quantities of interest are employed. Various LES-specific design criteria and combination of them are proposed, such as the time-averaged gradient of streamwise velocity, turbulent kinetic energy and production rate. These are investigated in the framework of elementary and balanced monitor functions. These are tested for the three-dimensional flow in a channel with periodic constrictions. The numerical results are compared to a highly resolved LES reference solution. The independence of the moving mesh method from the initial LES is shown, and its potential to improve the efficient resolution of turbulent flow features is demonstrated.
Tài liệu tham khảo
Beckett G., Mackenzie J.A.: Convergence analysis of finite difference approximations on equidistributed grids to a singularly perturbed boundary value problem. Appl. Numer. Math. 35(2), 87–109 (2000)
Berselli L., Iliescu T., Layton M.: Mathematics of Large Eddy Simulation of Turbulent Flows, 1st edn. Springer, Heidelberg (2006)
Breuer M., Peller N., Rapp C., Manhart M.: Flow over priodic hills—numerical and experimental study in a wide range of Reynolds numbers. Comput. Fluids 38(2), 433–457 (2009)
Cao W., Huang W., Russell R.: An error indicator monitor function for an r-adaptive finite-element method. J. Comput. Phys. 170, 871–892 (2001)
Demirdžić I., Perić M.: Space conservation law in finite volume calculations of fluid flow. Int. J. Numer. Methods Fluids 8, 1037–1050 (1988)
Ducros, F., Nicoud, F., Poinsot, T.: Wall-adapting Local Eddy-Viscosity Models for Simulations in Complex Geometries. Numerical Methods for Fluid Dynamics VI, pp. 293–299. Oxford University Computing Laboratory, Wolfson Building, Parks Road, Oxford (1998)
Dvinsky A.: Adaptive grid generation from harmonic maps on Riemannian manifolds. J. Comput. Phys. 95(2), 450–476 (1991)
Ferziger J.H., Peric M.: Computational Methods for Fluid Dynamics, 3rd edn. Springer, Berlin (2002)
Fröhlich J.: Large Eddy Simulation Turbulenter Strömungen (in German), 1st edn. Teubner Verlag, Stuttgart (2006)
Fröhlich J., Mellen C.P., Rodi W., Temmerman L., Leschziner M.A.: Highly resolved large-eddy simulation of separated flow in a channel with streamwise periodic constrictions. J. Fluid Mech. 526, 19–66 (2005)
Fröhlich J., Terzi D.: Hybrid LES/RANS methods for the simulation of turbulent flows. Prog. Aerosp. Sci. 44(5), 349–377 (2008)
Germano M., Piomelli U., Moin P., Cabot W.H.: A dynamic subgrid-scale eddy viscosity model. Phys. Fluids A Fluid Dyn. 3(7), 1760–1765 (1991)
Geurts B.J., Fröhlich J.: A framework for predicting accuracy limitations in large-eddy simulation. Phys. Fluids 14(6), L41–L44 (2002)
Hertel, C., Schümichen, M., Lang, J., Fröhlich, J.: Using a moving mesh PDE for cell centres to adapt a finite volume grid. Flow Turbul. Combust. (2011, submitted)
Hinterberger C., Fröhlich J., Rodi W.: Three-dimensional and depth-averaged large-eddy simulations of some shallow water flows. J. Hydraul. Eng. 133, 857–872 (2007)
Huang W.: Practical aspects of formulation and solution of moving mesh partial differential equations. J. Comput. Phys. 171, 753–775 (2001)
Huang W., Russell R.D.: A high dimensional moving mesh strategy. Appl. Numer. Math. 26(1–2), 63–76 (1998)
Huang W., Russell R.D.: Moving mesh strategy based on a gradient flow equation for two-dimensional problems. SIAM J. Sci. Comput. 20(3), 998–1015 (1999)
Huang W., Russell R.D.: Adaptive Moving Mesh Methods, 1st edn. Springer, New York (2011)
Lang J., Cao W., Huang W., Russell R.D.: A two-dimensional moving finite element method with local refinement based on a posteriori error estimates. Appl. Numer. Math. 46, 75–94 (2003)
Leonard A.: Energy cascade in large-eddy simulations of turbulent fluid flows. Adv. Geophys. 18A, 16–42 (1974)
Mason P.J., Callen N.S.: On the magnitude of the subgrid-scale eddy coefficient in large-eddy simulations of turbulent channel flow. J. Fluid Mech. 162, 439–462 (1986)
Mellen, C.P., Fröhlich, J., Rodi, W.: Large eddy simulation of the flow over periodic hills. In: 16th IMACS World Congress (2000)
Pope S.: Turbulent Flows. Cambridge University Press, Cambridge, MA (2000)
Rapp C., Manhart M.: Flow over periodic hills: an experimental study. Exp. Fluids 51(1), 247–269 (2011). doi:10.1007/s00348-011-1045-y
Rhie C.M., Chow W.L.: Numerical study of the turbulent flow past an airfoil with trailing edge separation. AIAA J. 21, 1525–1532 (1983)
Sagaut P.: Large Eddy Simulation of Incompressible Flows. Springer, Berlin (2001)
Smagorinsky J.: General circulation experiments with the primitive equations, I, the basic experiment. Mon. Weather Rev. 91, 99–164 (1963)
Stone H.L.: Iterative solution of implicit approximation of multidimensional partial differential equations. SIAM J. Numer. Anal. 5, 530–558 (1968)
Temmerman L., Leschziner M.A., Mellen C.P., Fröhlich J.: Investigation of wall-function approximations and subgrid-scale models in large eddy simulation of separated flow in a channel with streamwise periodic constrictions. Int. J. Heat Fluid Flow 24, 157–180 (2003)
van Dam, A.: Go with the flow. Ph.D. thesis, Utrecht University (2009)
Werner, H., Wengle, H.: Large-eddy simulation of turbulent flow over and around a cube in a plane channel. In: Durst, F., Friedrich, R., Launder, B., Schmidt, F., Schumann, U., Whitelaw, J. (eds.) Selected Papers from the 8th Symposium on Turbulent Shear Flows, pp. 155–168. Springer (1993)
Winslow A.M.: Numerical solution of the quasilinear poisson equation in a nonuniform triangle mesh. Journal of Computational Physics 2, 149–172 (1967)
Zhu J., Rodi W.: Computation of axisymmetric confined jets in a diffuser. Int. J. Numer. Methods Fluids 14, 241–251 (1992)