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

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), 1:73–100.
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