Finite volume method

Finite volume methods (FVM) are commonly used for numerical solution of conservation laws. Most of the laws of nature can be written in conservation form like conservation of mass, momentum, energy and charge. A conservation law for a conserved quantity u can be simply stated as:

The basic steps in a finite volume method are:

• Divide the computational domain into finite volumes. This is known as grid generation.
• Apply the conservation law to each finite volume. This requires the computation of the flux across the boundary of each finite volume.
• Solve the resulting system of equations by some suitable method.

• Introduction to finite volume method: Slides of a talk I gave on finite volume method at Annamalai University.