UUM601E: ADVANCED COMPUTATIONAL FLUID DYNAMICS

Fall
Thursday 9:30-12:30
Location: UUBF Computer Lab.
Syllabus


Reference Books:
-High-Resolution Methods for Incompressible and Low-Speed Flows, Dimitris Drikakis and William Rider.
Electronic version is available through ScienceDirect.
-Numerical Computation of Internal and External Flows. Volume 1: Fundamentals of Numerical Discretization, Charles Hirch.
Electronic version is available through ScienceDirect.
-Computational Methods for Fluid Dynamics, Joel H. Ferziger and Milovan Peric.
-Computational Fluid Dynamics: Principles and Applications, Jiri Blazek.
-Computational Fluid Mechanics and Heat Transfer, John C. Tannehill, Dale A. Anderson and Richard H. Pletcher.
-High-Order Methods for Incompressible Fluid Flow, Michel O. Deville, Paul F. Fischer and Ernest H. Mund.
-Spectral / hp element methods for CFD, George Karniadakis and Spencer J. Sherwin.
Electronic version is availablet hrough ScienceDirect.


PROJECTS

Project #1

Project #2

Project #3


SUGGESTED FURTHER READINGS

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  • D. J. Mavriplis, Unstructured grid techniques. Annul. Rev. Fluid Mech. (1997), 29:473-514.
  • F. H. Harlow and J. E. Welch, Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface. J. Comput. Phys., (1965), 8:2182–2189.
  • R. Mittal, H. Dong, M. Bozkurttas, F. M. Najjar, A. Vargas and A. von Loebbecke, A versatile sharp interface immersed boundary method for incompressible flows with complex boundaries. J. Comput. Phys., (2008), 227:4825–4852.
  • C. S. Peskin, The immersed boundary method. Acta Numerica, (2002), 11:479–517.
  • K. Mahesh, G. Constantinescu and P. Moin, A numerical method for large-eddy simulation in complex geometries. J. Comput. Phys., (2004), 197:215–240.
  • C. A. Hall, J. C. Cavendish and W. H. Frey, The dual variable method for solving fluid flow difference equations on delaunay triangulations. Comp. & Fluids (1991), 20:145–164.
  • R. A. Nicolaides, Direct discretizations of planar div–curl problems. SIAM J. Numer. Anal., (1992), 29:32–56.
  • C. W. Hirt, A. A. Amsden and J. L. Cook, An arbitrary Lagrangian–Eulerian computing method for all flow speeds. J. Comput. Phys., (1974), 14:227–253.
  • S. P. Vanka,  B. C.-J. Chen and W. T. Sha, A semi-implicit calculation procedure for flows described in boundary fitted coordinate systems. Numer. Heat Trans., (1980), 3:1–19.
  • S. Rida, F. McKenty, F. L. Meng and M. Reggio, A staggered control volume scheme for unstructured triangular grids. Int. J. Numer. Meth. Fluids, (1997), 25:697–717.
  • M. Thomadakis and M. A. Leschziner, Pressure-correction method for the solution of incompressible viscous flows on unstructured grids, Int. J. Numer. Meth. Fluids, (1996), 22:581–601.
  • R. L. Sani, P. M. Gresho, R. L. Lee and D. F. Griffiths, The cause and cure (?) of the spurious pressure generated by certain FEM solutions of the incompressible Navier-Stokes equations: Part 1. Int. J. Numer. Meth. Fluids, (1981), 1:17–43.
  • C. Prakash and S. V. Patankar, A control volume-based finite-element method for solving the Navier-Stokes equations using equal-order velocity-pressure interpolation. Numer. Heat Transfer, (1985), 8:259–280.
  • C. M. Rhie and W. L. Chow, Numerical study of the turbulent flow past an airfoil with trailing edge separation. AIAA J., (1983), 21:1525–1532.
  • G. Kim and H. Choi, A second-order time-accurate finite volume method for unsteady incompressible flow on hybrid unstructured grids. J. Comput. Phys., (200), 162:411–428.
  • T. M. Shih, C. H. Tan and B. C. Hwang, Effects of grid staggering on numerical schemes. Int. J. Numer. Meth. Fluids, (1989), 9:193–212.
  • A. J. Chorin, A numerical method for solving incompressible viscous flow problems. J. Comput. Phys. (1967), 2:12–26.
  • W. J. Rider, Approximate projection methods for incompressible flow: Implementation, variants and robustness. LA-UR-94-2000, Los Alamos National Laboratory, (1995)
  • P. R. Schunk, M. A. Heroux, R. R. Rao, T. A. Baer, S. R. Subia and A. C. Sun, Iterative solvers and preconditioners for fully-coupled finite element formulations of incompressible fluid mechanics and related transport problems. SAND2001-3512J, Sandia National Laboratories Albuuquerque, New Mexico, (2001).
  • M. Benzi, G. H. Golub and J. Liesen, Numerical solution of saddle point problems. Acta Numer., (2005), 14:1–137. 
  • H. C. Elman, V. E. Howle, J. N. Shadid and R. S. Tuminaro, A parallel block multi-level preconditioner for the 3D incompressible Navier–Stokes equations. J. Comput. Phys. (2003) 187:504–523. G. 
  • Tryggvason, B. Bunner, A. Esmaeeli, D. Juric, N. Al-Rawahi, W. Tauber, J. Han, S. Nas, Y. -J. Jan, A fron-tracking method for the computations of multiphase flow. J. Comput. Phys. (2001), 169:708–759. 
  • M. Sussman, E. Fatemi E, P. Smereka and S. Osher, An improved level set method for incompressible two-phase flows. Comp. & Fluids, (1998), 27:663–680. 
  • C. W. Hirt and B. D. Nichols, Volume of fluid (VOF) method for the dynamics of free boundaries. J. Comput. Phys. (1981), 39:201–225. 
  • C. Taylor and P. Hood, A numerical solution of the Navier-Stokes equations using the finite element technique. Comp. & Fluids, (1973), 1:73–100.
  • M. Crouzeix and P.A. Raviart, Conforming and nonconforming finite element methods for solving the stationary Stokes equations. RARIO Anal. Numer. (1973), 7:33–36.
  • A. N. Brooks and T. J. R. Hughes, Streamline upwind/Petrov-Galerkin formulations for convective dominated flows with particular emphasis on the incompressible Navier-Stokes equations. Comput. Meth. Appl. Mech. Eng., (1982), 32:199–259.
  • T. E. Tezduyar, S. Mittal, S. E. Ray and R. Shih, Incompressible flow computations with stabilized bilinear and linear equal-order interpolation velocity-pressure elements. Comput. Meth. Appl. Mech.  Eng. (1992), 95:221–242.
  • T, J. R. Hughes, L. P. Franca and G. M. Hulbert, A new finite element formulation for computational fluid dynamics: VII. The Galerkin/Least-squares method for advective-diffusive equations. Comput. Meth. Appl. Mech. Eng. (1989), 73:173–189.
  • A. Harten, B. Engquist, S. Osher and S. Chakravarthy, Uniformly high order essentially non-oscillatory schemes III. J. Comput. Phys. , (1987), 71:231–303.
  • A. Patera, A spectral element method for fluid dynamics: Laminar flow in a channel expansion. J. Comput. Phys. , (1984), 54:468–488.
  • W. H. Reed and T. R. Hill, Triangular mesh methods for the neutron transport equation. LA-UR-73-479, Los Alamos Scientific Laboratory, (1973).
  • Z. J. Wang, Spectral (finite) volume method for conservation laws on unstructured grids: Basic formulation. J. Comput. Phys., (2002), 178:210–251.
  • J. L. Steger and R. F. Warming, Flux vector splitting of the inviscid gasdynamic equations with application to finite-difference methods. J. Comput. Phys., (1981), 40:263–293.
  • P. L. Roe, Approximate Riemann solvers, parameter vectors and difference schemes. J. Comput. Phys., (1981), 43:357–372.
  • W. K. Anderson, J. L. Thomas and B. van Leer, Comparision of finite flux vector splitting for the Euler equations. AIAA  J., (1986), 24:1453–1460.
  • M. S. Liou and C. J. Steffen, A new flux splitting scheme. NASA-TM-104404.
  • W. K. Anderson, R. D. Rausch and D. L. Bonhaus, Implicit/multigrid algorithms for incompressible turbulent flows on unstructured grids. J. Comput. Phys., (1996), 128:391–408.
  • T. J. Barth,  Aspects of unstructured grids and finite-volume solvers for the Euler and Navier-Stokes equations.  Lecture Notes Presented at the VKI Lecture Series 1994-05, February.
  • T. H. Pulliam, Implicit Finite-Difference Methods for Euler Equations. Editor: W. G. Habashi,  Advanced in Computational Transonic. Pineridge Press. Volume 4 in the Series. Pages:503–543.
  • J. M. McDonough, Introductory lectures on turbulence physics, mathematics and modeling. Department of Mechanical Engineering and Mathematics, University of Kentucky, 2007.


    • SOME USEFUL LINKS:
    BLAS (Basic Linear Algebra Subprograms)
    LAPACK (Linear Algebra PACKage)
    The Message Passing Interface (MPI) standard
    Portable, Extensible Toolkit for Scientific Computation (PETSc)
    HYPRE: Scalable Linear Solvers and Multigrid Methods
    MUltifrontal Massively Parallel sparse direct Solver (MUMPS)
    Geometry and Mesh Generation Toolkit (CUBIT)
    A three-dimensional finite element mesh generator with built-in pre- and ğost-processing facilities - GMSH
    Standford Open Source CFD Code - SU2
    Incompressible Flow & Iterative Solver Software (IFISS)
    The Software Packages Feat/Feast/FeatFlow
    The Open Source CFD Toolbox (OpenFOAM)
    CFD Online