Abstract
This paper presents an anisotropic adaptive strategy for CFD that combines a nearly body-fitted mesh strategy with an iterative anisotropic adaptation to the flow solution. The nearly body-fitted mesh method consists in modelling embedded interfaces by a level-set representation in combination with local anisotropic mesh refinement and mesh adaptation (Quan et al. in Comput Methods Appl Mech Eng 268:65–81, 2014). The generated nearly body-fitted meshes are used to perform CFD simulations. Besides, anisotropic mesh adaptation based on the Hessian of the flow solution is used to improve the accuracy of the solution. We show that the method is beneficial in challenging CFD simulations involving complex geometries and time dependent flow, as it suppresses the need for the tedious process of body-fitted mesh generation, without altering the finite element formulation nor the prescription of boundary conditions. The methodology yields accurate flow solutions for a reasonable computational cost, despite very limited user interaction.
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References
Alauzet F (2010) Size gradation control of anisotropic meshes. Finite Elem Anal Des 46(1–2):181–202
Balay S, Brown J, Buschelman K, Gropp WD, Kaushik D, Knepley MG, Curfman McInnes L, Smith BF, Zhang H (2013) PETSc Web page. http://www.mcs.anl.gov/petsc
Barbosa HJC, Thomas JRH (1991) The finite element method with Lagrange multipliers on the boundary: circumventing the Babuska-Brezzi condition. Comput Methods Appl Mech Eng 85(1):109–128
Beran P (1991) Steady and unsteady solutions of the Navier-Stokes equations for flows about airfoils at low speeds. AIAA Paper 91–1733
Borouchaki H, Georges PL, Hecht F, Laug P, Saltel P (1997) Delaunay mesh generation governed by metric specifications. part I. algorithms. Finite Elem Anal Des 25(61–83):85–109
Burleson AC, Turitto VT (1996) Identification of quantifiable hemodynamic factors in the assessment of cerebral aneurysm behavior. Thromb Haemost 76:118–123
Calhoun D (2002) A Cartesian grid method for solving the two-dimensional streamfunction-vorticity equations in irregular regions. J Comput Phys 176:231–275
Choi JI, Oberoi RC, Eewards JR, Rosati JA (2007) An immersed boundary method for complex incompressible flows. J Comput Phys 224:757–784
Cignoni P, Rocchini C, Scopigno R (1998) Metro: measuring error on simplified surfaces. Comput Graph Forum 17(2):167–174
Claisse A, Ducrot V, Frey P (2009) Levelsets and anisotropic mesh adaptation. Discret Contin Dyn Syst 23(1–2):165–183
Coutanceau M, Bouard R (1977) Experimental determination of the main features of the viscous flow in the wake of a circular cylinder in uniform translation. part 1, steady flow. J Fluid Mech 79(2):231–256
Dennis SCR, Chang G-Z (1970) Numerical solutions for steady flow past a circular cylinder at Reynolds number up to 100. J Fluid Mech 42:471–489
Dobrzynski C, Frey P (2008) Anisotropic Delaunay mesh adaptation for unsteady simulations. In: Proceedings of the 17th international meshing roundtable, pp 177–194
Dolbow JE, Franca LP (2008) Residual-free bubbles for embedded Dirichlet problems. Comput Methods Appl Mech Eng 197:3751–3759
Dolbow JE, Harari I (2009) An efficient finite element method for embedded interface problems. Int J Numer Methods Eng 78(2):229–252
Fornberg B (1980) A numerical study of steady viscous flow past a circular cylinder. J Fluid Mech 98(4):819–855
Frey P, Alauzet F (2005) Anisotropic mesh adaptation for CFD computations. Comput Methods Appl Mech Eng 194(48–49):5068–5082
Geller S, Krafczyk M, Tolke J, Turek S, Hron J (2005) Benchmark computations based on lattice-Boltzmann, finite element and finite volume methods for laminar flows. Comput Fluids 35:888–897
Geuzaine C, Remacle JF (2009) Gmsh: a three dimensional finite element mesh generator with built-in pre-and post-processing facilities. Int J Numer Methods Eng 79:1309–1331
Hachem E, Kloczko T, Digonnet H, Coupez T (2012) Stabilized finite element solution to handle complex heat and fluid flows in industrial furnaces using the immersed volume method. Int J Numer Methods Fluids 68(1):99–121
Hautefeuille M, Annavarapu C, Dolbow JE (2011) Robust imposition of Dirichlet boundary conditions on embedded surfaces. Int J Numer Methods Eng 90(1):40–64
Hecht F (2006) Bamg: Bidimensional anisotropic mesh generator. http://www.freefem.org/ff++
Ilinca F, Hétu J-F (2011) A finite element immersed boundary method for fluid flow around rigid objects. Int J Numer Methods Fluids 65:856–875
Krams R, Wentzel JJ, Oomen JAF, Vinke R, Schuurbiers JCH, de Feyter PJ, Serruys PW, Slager CJ (1997) Evaluation of endothelial shear stress and 3D geometry as factors determining the development of atherosclerosis and remodeling in human coronary arteries in vivo. Arterioscl Thromb Vasc Biol 17:2061–2065
Le D-V, Khoo B-C, Lim K-M (2008) An implicit-forcing immersed boundary method for simulating viscous flows in irregular domains. J Comput Methods Appl Mech Eng 197:2119–2130
Lima ALF, Silva E, Silveira-Neto A, Damasceno JJR (2003) Numerical simulation of two-dimensional flows over a circular cylinder using the immersed boundary method. J Comput Phys 189:351–370
Marchandise E, Crosetto P, Geuzaine C, Remacle J-F, Sauvage E (2011) Quality open source mesh generation for cardiovascular flow simulations. In: Volume accepted of springer series on modeling, simulation and applications, chapter of modelling physiological flows. Springer, Berlin.
Marchandise E, Remacle J-F (2006) A stabilized finite element method using a discontinous level set approach for solving two phase incompressible flows. J Comput Phys 219(2):780–800
Mavriplis D, Jameson A (1987) Multigrid solution of the two-dimensional Euler equations on unstructured triangular meshes. AIAA paper 87–0353
Pagnutti D, Ollivier-Gooch C (2010) Delaunay-based anisotropic mesh adaptation. Eng Comput 26:407–4185
Park J, Kwon K, Choi H (1998) Numerical solutions of flow past a circular cylinder at Reynolds numbers up to 160. KSME Int J 12(6):1200–1205
Pulliam TH (1985) Efficient solution methods for the Navier-Stokes equations. Lecture Notes for the von Kármán Institute For Fluid Dynamics Lecture Series: Numerical Techniques for Viscous Flow Computation In Turbomachinery Bladings, von Kármán Institute, Rhode-St-Geness, Belgium
Quan D-L, Toulorge T, Marchandise E, Remacle J-F, Bricteux G (2014) Anisotropic mesh adaptation with optimal convergence for finite elements using embedded geometries. Comput Methods Appl Mech Eng 268:65–81
Radespiel R (1987) A cell-vertex multigrid method for the Navier-Stokes equations. NASA TM-101557
Remacle J-F, Li X, Chevaugeon N, Shephard MS (2002) Transient mesh adaptation using conforming and non conforming mesh modifications. In: Sandia National Laboratories (ed) Proceedings of the 11th international meshing roundtable, Sept 15–18
Russell D, Wang Z-J (2003) A Cartesian grid method for modeling multiple moving objects in 2D incompressible viscous flow. J Comput Phys 191:177–205
Sauvage E (2014) Patient-specific blood flow modelling. Ph. D. Thesis, Université catholique de Louvain
Schlichting H (1960) Boundary layer theory. McGraw-Hill Book Company Inc, New York
Shaaban AM, Duerinckx AJ (2000) Wall shear stress and early atherosclerosis. Am J Roentgenol 174:1657–1665
Sucker D, Brauer H (1975) Fluiddynamik bei querangeströmten Zylindern. Wärme- und Stoffübertragung 8:149–158
Tritton D-J (1959) Experiments on the flow past a circular cylinder at low Reynolds numbers. J Fluid Mech 6(4):547–567
Turkel E, Radespiel R, Kroll N (1997) Assessment of preconditioning methods for multidimensional aerodynamics. Comput Fluids 26(6):613–634
Wieselsberger C (1922) New data on the laws of fluid resistance. NACA TN 84
Ye T (1999) An accurate Cartesian grid method for viscous incomressible flows with complex immersed boundary. J Comput Phys 156:209–240
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Quan, DL., Toulorge, T., Bricteux, G. et al. Anisotropic adaptive nearly body-fitted meshes for CFD. Engineering with Computers 30, 517–533 (2014). https://doi.org/10.1007/s00366-014-0360-3
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DOI: https://doi.org/10.1007/s00366-014-0360-3