Adaptive boundary layer meshing for viscous flow simulations

A procedure for anisotropic mesh adaptation accounting for mixed element types and boundary layer meshes is presented. The method allows to automatically construct meshes on domains of interest to accurately and efficiently compute key flow quantities, especially near wall quantities like wall shear stress. The new adaptive approach uses local mesh modification procedures in a manner that maintains layered and graded elements near the walls, which are popularly known as boundary layer or semi-structured meshes, with highly anisotropic elements of mixed topologies. The technique developed is well suited for viscous flow applications where exact knowledge of the mesh resolution over the computational domain required to accurately resolve flow features of interest is unknown a priori. We apply the method to two types of problem cases; the first type, which lies in the field of hemodynamics, involves pulsatile flow in blood vessels including a porcine aorta case with a stenosis bypassed by a graft whereas the other involves high-speed flow through a double throat nozzle encountered in the field of aerodynamics.

[1]  John B. Shoven,et al.  I , Edinburgh Medical and Surgical Journal.

[2]  S. Dey,et al.  Hierarchical basis for stabilized finite element methods for compressible flows , 2003 .

[3]  Kazuhiro Nakahashi,et al.  Unstructured Mesh Generation For Viscous Flow Computations , 2002, IMR.

[4]  O. C. Zienkiewicz,et al.  Adaptive remeshing for compressible flow computations , 1987 .

[5]  Tommy Minyard,et al.  Adaptive hybrid grid methods , 2000 .

[6]  David A Steinman,et al.  Finite-element modeling of the hemodynamics of stented aneurysms. , 2004, Journal of biomechanical engineering.

[7]  Shahyar Pirzadeh,et al.  Unstructured Viscous Grid Generation by Advancing-Layers Method , 1993 .

[8]  Pascal Frey,et al.  Anisotropic mesh adaptation for CFD computations , 2005 .

[9]  J. Remacle,et al.  Anisotropic adaptive simulation of transient flows using discontinuous Galerkin methods , 2005 .

[10]  T. Hughes,et al.  Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations , 1990 .

[11]  Gustavo C. Buscaglia,et al.  Anisotropic mesh optimization and its application in adaptivity , 1997 .

[12]  Charles A. Taylor,et al.  A coupled momentum method for modeling blood flow in three-dimensional deformable arteries , 2006 .

[13]  Y. Saad,et al.  GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems , 1986 .

[14]  Kenneth E. Jansen,et al.  A stabilized finite element method for the incompressible Navier–Stokes equations using a hierarchical basis , 2001 .

[15]  T. Hughes,et al.  A new finite element formulation for computational fluid dynamics: I. Symmetric forms of the compressible Euler and Navier—Stokes equations and the second law of thermodynamics , 1986 .

[16]  Mark S. Shephard,et al.  Boundary layer mesh generation for viscous flow simulations , 2000 .

[17]  Mark S. Shephard,et al.  3D anisotropic mesh adaptation by mesh modification , 2005 .

[18]  Rainald Löhner,et al.  Generation of non‐isotropic unstructured grids via directional enrichment , 2000 .

[19]  Charles A. Taylor,et al.  Efficient anisotropic adaptive discretization of the cardiovascular system , 2006 .

[20]  S. Connell,et al.  Semistructured mesh generation for three-dimensional Navier-Stokes calculations , 1995 .

[21]  Mark S. Shephard,et al.  On Anisotropic Mesh Generation and Quality Control in Complex Flow Problems , 2001, IMR.

[22]  Jacques Periaux,et al.  Presentation of Problems and Discussion of Results , 1987 .

[23]  Thomas J. R. Hughes,et al.  Finite element modeling of blood flow in arteries , 1998 .

[24]  Frédéric Hecht,et al.  Anisotropic unstructured mesh adaption for flow simulations , 1997 .

[25]  Mark S. Shephard,et al.  Accounting for curved domains in mesh adaptation , 2003 .

[26]  J. Womersley.  Method for the calculation of velocity, rate of flow and viscous drag in arteries when the pressure gradient is known , 1955, The Journal of physiology.

[27]  Yannis Kallinderis,et al.  Hybrid grid generation for turbomachinery and aerospace applications , 2000 .

[28]  G. Hulbert,et al.  A generalized-α method for integrating the filtered Navier–Stokes equations with a stabilized finite element method , 2000 .

[29]  Xiangrong Li,et al.  Anisotropic adaptive finite element method for modelling blood flow , 2005, Computer methods in biomechanics and biomedical engineering.

[30]  T. Hughes,et al.  A new finite element formulation for computational fluid dynamics: II. Beyond SUPG , 1986 .

[31]  Charles A. Taylor,et al.  In Vivo Validation of Numerical Prediction of Blood Flow in Arterial Bypass Grafts , 2002, Annals of Biomedical Engineering.

[32]  C.R.E. de Oliveira,et al.  Tetrahedral mesh optimisation and adaptivity for steady-state and transient finite element calculations , 2001 .

[33]  Thomas J. R. Hughes,et al.  A new finite element formulation for computational fluid dynamics: IV. A discontinuity-capturing operator for multidimensional advective-diffusive systems , 1986 .

[34]  Carl Ollivier-Gooch,et al.  Tetrahedral mesh improvement using swapping and smoothing , 1997 .

[35]  Yannis Kallinderis,et al.  A dynamic adaptation scheme for general 3-D hybrid meshes , 2005 .

[36]  Charles A. Taylor,et al.  Outflow boundary conditions for three-dimensional finite element modeling of blood flow and pressure in arteries , 2006 .

[37]  C. Taylor,et al.  Predictive medicine: computational techniques in therapeutic decision-making. , 1999, Computer aided surgery : official journal of the International Society for Computer Aided Surgery.