ADVANCED COMPUTATIONAL FLUID DYNAMICS
Location: UUBF Computer Lab.
-High-Resolution Methods for Incompressible and Low-Speed
Flows, Dimitris Drikakis and William Rider.
version is available through ScienceDirect.
-Numerical Computation of Internal and External Flows.
Volume 1: Fundamentals of Numerical Discretization, Charles Hirch.
version is available through ScienceDirect.
-Computational Methods for Fluid Dynamics, Joel H. Ferziger
and Milovan Peric.
-Computational Fluid Dynamics: Principles and Applications, Jiri
-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.
version is availablet hrough ScienceDirect.
SUGGESTED FURTHER READINGS
J. L. Steger and R. L. Sorenson,
Automatic mesh-point clustering near a boundary in grid generation with
elliptic partial differential equations. J. Comput.
D. J. Mavriplis, Unstructured
grid techniques. Annul. Rev. Fluid
Mech. (1997), 29:473-514.
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.
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),
Peskin, The immersed boundary method. Acta
Numerica, (2002), 11:479–517.
G. Constantinescu and P. Moin, A numerical method for large-eddy simulation
in complex geometries. J. Comput. Phys.,
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.
Nicolaides, Direct discretizations of planar div–curl problems. SIAM J. Numer. Anal., (1992), 29:32–56.
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.
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.
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.
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.
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.
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),
Rhie and W. L. Chow, Numerical study of the turbulent flow past an airfoil
with trailing edge separation. AIAA
J., (1983), 21:1525–1532.
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.
Shih, C. H. Tan and B. C. Hwang, Effects of grid staggering on numerical schemes.
Int. J. Numer. Meth. Fluids, (1989),
Chorin, A numerical method for solving incompressible viscous flow problems.
J. Comput. Phys. (1967), 2:12–26.
Rider, Approximate projection methods for incompressible flow: Implementation,
variants and robustness. LA-UR-94-2000,
Los Alamos National Laboratory, (1995)
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).
G. H. Golub and J. Liesen, Numerical solution of saddle point problems.
Acta Numer., (2005), 14:1–137.
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.
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.
E. Fatemi E, P. Smereka and S. Osher, An improved
level set method for incompressible two-phase flows. Comp. & Fluids, (1998), 27:663–680.
Hirt and B. D. Nichols, Volume of fluid (VOF) method for the dynamics of
free boundaries. J. Comput. Phys. (1981),
C. Taylor and P.
Hood, A numerical solution of the Navier-Stokes equations using the finite element technique.
& 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.
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.,
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.
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),
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
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.,
Liou and C. J. Steffen, A new flux splitting scheme. NASA-TM-104404.
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.
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.
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.
McDonough, Introductory lectures on turbulence physics, mathematics and modeling.
Department of Mechanical Engineering and Mathematics, University of Kentucky,
SOME USEFUL LINKS:
BLAS (Basic Linear Algebra Subprograms)
LAPACK (Linear Algebra PACKage)
Passing Interface (MPI) standard
Portable, Extensible Toolkit for
Scientific Computation (PETSc)
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
Incompressible Flow & Iterative Solver Software (IFISS)
The Open Source CFD Toolbox (OpenFOAM)