# Finite volume

(Difference between revisions)
 Revision as of 18:53, 5 December 2005 (view source)Jola (Talk | contribs)m← Older edit Revision as of 08:10, 17 February 2006 (view source)Newer edit → Line 3: Line 3: The most compelling feature of the FVM is that the resulting solution satisfies the conservation of quantities such as mass, momentum, energy, and species. This is '''exactely''' satisfied for any control volume as well as for the whole computational domain and '''for any number of control volumes'''. Even a coarse grid solution exhibits exact integral balances.
The most compelling feature of the FVM is that the resulting solution satisfies the conservation of quantities such as mass, momentum, energy, and species. This is '''exactely''' satisfied for any control volume as well as for the whole computational domain and '''for any number of control volumes'''. Even a coarse grid solution exhibits exact integral balances.
---- ---- + + == External links == + * [http://www.imtek.uni-freiburg.de/simulation/mathematica/imsReferencePointers/FVM_introDocu.html The Finite Volume Method (FVM) - An introduction] by Oliver Rübenkönig of Albert Ludwigs University of Freiburg, available under the GNU Free Document License|GFDL. + + Return to [[Numerical methods | Numerical Methods]] Return to [[Numerical methods | Numerical Methods]] {{stub}} {{stub}}

## Revision as of 08:10, 17 February 2006

The Finite Volume Method (FVM) is one of the most versatile discretization techniques used in CFD. Based on the control volume formulation of analytical fluid dynamics, the first step in the FVM is to divide the domain into a number of control volumes (aka cells, elements) where the variable of interest is located at the centroid of the control volume. The next step is to integrate the differential form of the governing equations (very similar to the control volume approach) over each control volume. Interpolation profiles are then assumed in order to describe the variation of the concerned variable between cell centroids. The resulting equation is called the discretized or discretization equation. In this manner, the discretization equation expresses the conservation principle for the variable inside the control volume.

The most compelling feature of the FVM is that the resulting solution satisfies the conservation of quantities such as mass, momentum, energy, and species. This is exactely satisfied for any control volume as well as for the whole computational domain and for any number of control volumes. Even a coarse grid solution exhibits exact integral balances.