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

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 available
t hrough ScienceDirect.


Project #1

Project #2

Project #3


  • J. L. Steger and R. L. Sorenson, Automatic mesh-point clustering near a boundary in grid generation with elliptic partial differential equations. J. Comput. Phys., (1979), 33:405–410.
  • 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), 1:73100.
  • M. Crouzeix and P.A. Raviart, Conforming and nonconforming finite element methods for solving the stationary Stokes equations. RARIO Anal. Numer. (1973), 7:3336.
  • 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), 32:199259.
  • 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), 95:221242.
  • 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), 73:173189.
  • A. Harten, B. Engquist, S. Osher and S. Chakravarthy, Uniformly high order essentially non-oscillatory schemes III. J. Comput. Phys. , (1987), 71:231303.
  • A. Patera, A spectral element method for fluid dynamics: Laminar flow in a channel expansion. J. Comput. Phys. , (1984), 54:468488.
  • 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), 178:210251.
  • 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), 40:263293.
  • P. L. Roe, Approximate Riemann solvers, parameter vectors and difference schemes. J. Comput. Phys., (1981), 43:357372.
  • 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.

    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