Navier-Stokes --- Runge-Kutta
 

OK, here's an archived thread I thought I'd resurrect

http://www.cfd-online.com/Forum/main...cgi?read=32057

Here's a continuation thread ...

There are many people who use explicit Runge-Kutta methods for the Navier-Stokes Equations. This one has tons of detail for explicit methods:

http://techreports.larc.nasa.gov/ltrs/1999-cit.html ( Go down to 133; ICASE Report 99-22)

Here are some people who cite Williamsons paper:

http://scholar.google.com/scholar?q=low-storage+Williamson+Navier&ie=UTF-8&oe=UTF-8&hl=en

Here are some papers for implicit Runge-Kutta methods applied to the Navier-Stokes Equations:

http://techreports.larc.nasa.gov/ltr...-2001-2612.pdf

http://techreports.larc.nasa.gov/ltr...-2002-3346.pdf

http://fun3d.larc.nasa.gov/papers/carpenter.pdf

There are many kinds of implicit Runge-Kutta methods:

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Diagonally Implicit Runge-Kutta (DIRK) methods

Singly Diagonally Implicit Runge-Kutta (SDIRK) methods

Explicit Singly Diagonally Implicit Runge-Kutta (ESDIRK) methods

Singly Implicit Runge-Kutta (SIRK) methods

Multiply Implicit Runge-Kutta (MIRK) methods

Mono Implicit Runge-Kutta (MIRK) methods

Gauss Implicit Runge-Kutta methods

Radau Implicit Runge-Kutta methods

Lobatto Implicit Runge-Kutta methods

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ESDIRKs are the most appropriate to large-scale CFD.

There are also implicit/explicit Runge-Kutta methods for the Navier-Stokes Equations:

http://portal.acm.org/citation.cfm?id=267001

http://portal.acm.org/citation.cfm?i...l=GUIDE&dl=ACM

http://portal.acm.org/citation.cfm?id=639155.639164