Finite element LES and VMS methods on tetrahedral meshes

Sagaut, 2006 Hughes, 1995, Multiscale phenomena: Green’s functions, the Dirichlet-to-Neumann formulation, subgrid-scale models, bubbles and the origin of stabilized methods, Comput. Methods Appl. Mech. Engrg., 127, 387, 10.1016/0045-7825(95)00844-9 Guermond, 1999, Stabilization of Galerkin approximations of transport equations by subgrid modeling, M2AN, 33, 1293, 10.1051/m2an:1999145 Hughes, 2000, Large Eddy simulation and the variational multiscale method, Comput. Visual. Sci., 3, 47, 10.1007/s007910050051 Smagorinsky, 1963, General circulation experiments with the primitive equations, Mon. Weather Rev., 91, 99, 10.1175/1520-0493(1963)091<0099:GCEWTP>2.3.CO;2 Germano, 1991, A dynamic subgrid-scale Eddy viscosity model, Phys. Fluids A, 3, 1760, 10.1063/1.857955 Lilly, 1992, A proposed modification of the Germano subgrid-scale closure method, Phys. Fluids A, 4, 633, 10.1063/1.858280 Leonard, 1974, Energy cascade in large Eddy simulation of turbulent fluid flows, Adv. Geophys., 18A, 237 Galdi, 2000, Approximation of the larger eddies in fluid motion II: A model for space filtered flow, Math. Models Methods Appl. Sci., 10, 343, 10.1142/S0218202500000203 John, 2004, vol. 34 John, 2005, An assessment of two models for the subgrid scale tensor in the rational LES model, J. Comp. Appl. Math., 173, 57, 10.1016/j.cam.2004.02.022 Iliescu, 2003, A numerical study of a class of LES models, Int. J. Comput. Fluid Dyn., 17, 75, 10.1080/1061856021000009209 Dunca, 2004, The commutation error of the space averaged Navier–Stokes equations on a bounded domain, 53 Berselli, 2006, Asymptotic behavior of commutation errors and the divergence of the Reynolds stress tensor near the wall in the turbulent channel flow, Math. Meth. Appl. Sci., 29, 1709, 10.1002/mma.750 Berselli, 2007, Analysis of commutation errors for functions with low regularity, J. Comput. Appl. Math., 206, 1027, 10.1016/j.cam.2006.09.011 John, 2006, Time-dependent flow across a step: The slip with friction boundary condition, Internat. J. Numer. Methods Fluids, 50, 713, 10.1002/fld.1074 Hughes, 2004, Multiscale and stabilized methods John, 2006, On large Eddy simulation and variational multiscale methods in the numerical simulation of turbulent incompressible flows, Appl. Math., 51, 321, 10.1007/s10778-006-0109-9 John, 2007, Simulations of the turbulent channel flow at Reτ=180 with projection-based finite element variational multiscale methods, Internat. J. Numer. Methods Fluids, 55, 407, 10.1002/fld.1461 V. John, A. Kindl, A variational multiscale method for turbulent flow simulation with adaptive large scale space. Universität des Saarlandes, Fachrichtung Mathematik, Preprint 228, 2009 V. John, A. Kindl, Numerical studies of finite element variational methods for turbulent flow simulations. Comput. Methods Appl. Mech. Engrg., 2009 (in press) John, 2005, A finite element variational multiscale method for the Navier–Stokes equations, SIAM J. Sci. Comput., 26, 1485, 10.1137/030601533 Hughes, 2001, The multiscale formulation of large Eddy simulation: Decay of homogeneous isotropic turbulence, Phys. Fluids, 13, 505, 10.1063/1.1332391 Hughes, 2001, Large Eddy simulation of turbulent channel flows by the variational multiscale method, Phys. Fluids, 13, 1784, 10.1063/1.1367868 Gravemeier, 2006, Scale-separating operators for variational multiscale large Eddy simulation of turbulent flows, J. Comput. Phys., 212, 400, 10.1016/j.jcp.2005.07.007 John, 2008, Variants of projection-based finite element variational multiscale methods for the simulation of turbulent flows, Internat. J. Numer. Methods Fluids, 56, 1321, 10.1002/fld.1712 Ramakrishnan, 2004, Turbulence control simulation using the variational multiscale method, AIAA J., 42, 745, 10.2514/1.9557 John, 2001, Higher order finite element discretizations in a benchmark problem for incompressible flows, Internat. J. Numer. Methods Fluids, 37, 885, 10.1002/fld.195 John, 2006, On the efficiency of linearization schemes and coupled multigrid methods in the simulation of a 3d flow around a cylinder, Internat. J. Numer. Methods Fluids, 50, 845, 10.1002/fld.1080 Bernardi, 1985, Analysis of some finite elements for the Stokes problem, Math. Comput., 44, 71, 10.1090/S0025-5718-1985-0771031-7 Pope, 2000 Meyers, 2006, On the model coefficients for the standard and the variational multi-scale smagorinsky model, J. Fluid Mech., 569, 287, 10.1017/S0022112006002850 Ladyzhenskaya, 1967, New equations for the description of motion of viscous incompressible fluids and solvability in the large of boundary value problems for them, Proc. Steklov Inst. Math., 102, 95 Świerczewska, 2006, A dynamical approach to large Eddy simulation of turbulent flows: Existence of weak solutions, Math. Methods Appl. Sci., 29, 99, 10.1002/mma.667 John, 2002, Analysis of numerical errors in large Eddy simulation, SIAM J. Numer. Anal., 40, 995, 10.1137/S0036142900375554 John, 2006, A two-level variational multiscale method for convection-dominated convection–diffusion equations, Comput. Methods Appl. Math. Engrg., 195, 4594, 10.1016/j.cma.2005.10.006 John, 2006, A comparison of time-discretization/linearization approaches for the time-dependent incompressible Navier–Stokes equations, Comput. Methods Appl. Mech. Engrg., 195, 5995, 10.1016/j.cma.2005.10.007 John, 2002, Higher order finite element methods and multigrid solvers in a benchmark problem for the 3D Navier–Stokes equations, Internat. J. Numer. Methods Fluids, 40, 775, 10.1002/fld.377 John, 2004, MooNMD — A program package based on mapped finite element methods, Comput. Visual. Sci., 6, 163, 10.1007/s00791-003-0120-1 Rodi, 1997, Status of large Eddy Simulation: Results of a workshop, J. Fluids Engrg., 119, 248, 10.1115/1.2819128 H. Si, Tetgen, A quality tetrahedral mesh generator and three-dimensional Delauny triangulator, v1.3 User’s Manual. Technical Report 9, Weierstrass Institute Berlin, 2004