OpenFOAM guide/Finite volume method

This article is about the finite volume method in general. For one specific to OpenFOAM, see 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.