View source for OpenFOAM guide/Finite volume method

{{About|the finite volume method in general|one specific to OpenFOAM|Finite volume method (OpenFOAM)}}
The finite volume method is a [[discretization]] scheme for a flow domain in which a set of equations apply.  The equations are usually non-linear, and for fluid problems, they are the transport equations.  The finite volume method subdivides the flow domain into a finite number of contiguous control volumes.  The method uses the integral forms of the equation set as a starting point.  These equations are integrated, usually using the [[midpoint rule]], although higher order schemes are available.  [[Gauss' theorem]] is often applied to the equations as well.  The result is a finite number of linear equations that can be solved using matrix methods.

The flow quantities are defined at one or a few locations within each volume, depending on the strategy employed:
* Co-located grids have all the fluid dynamic quantities defined at a single node in the control volume; and
* Staggered grids define volume based quantities (e.g. pressure, density, temperature) at a single point in the centre, and flux based quantities (i.e. velocity) on the faces.

Values at other locations in space are obtained from [[interpolation]].  Co-located grids require more [[interpolation]] than staggered grid, as quantities are the control volume faces must first be interpolated before integration can be performed.  Linear interpolation is second-order accurate, and is frequently used, although other interpolation methods are available.

[[Category:Numerical methods]]