Finite Volume Method

The finite volume method is a numerical method for solving partial differential equations that calculates the values of the conserved variables averaged across the volume. One advantage of the finite volume method over finite difference methods is that it does not require a structured mesh (although a structured mesh can also be used). Furthermore, the finite volume method is preferable to other methods as a result of the fact that boundary conditions can be applied noninvasively. This is true because the values of the conserved variables are located within the volume element, and not at nodes or surfaces. Finite volume methods are especially powerful on coarse nonuniform grids and in calculations where the mesh moves to track interfaces or shocks.

Hyman et al. (1992) have derived local, accurate, reliable, and efficient finite volume methods that mimic symmetry, conservation, stability, and the duality relationships between the gradient, curl, and divergence operators on nonuniform rectangular and cuboid grids.

REFERENCES:

Hyman, J. M.; Knapp, R.; and Scovel, J. C. "High Order Finite Volume Approximations of Differential Operators on Nonuniform Grids." Physica D 60, 112-138, 1992.

Rübenkönig, O. "The Finite Volume Method (FVM)." http://www.imtek.uni-freiburg.de/simulation/mathematica/imsReferencePointers/FVM_introDocu.htm.

Versteeg, H. K. and Malalasekera, W. An Introduction to Computational Fluid Dynamics: The Finite Volume Method. Reading, MA: Addison-Wesley, 1995.