The Finite Volume Method (FVM) is a numerical technique that transforms the partial differential equations representing conservation laws over differential volumes into discrete algebraic equations over finite volumes (or elements or cells). In a similar fashion to the finite difference or finite element method, the first step in the solution process is the discretization of the geometric domain, which, in the FVM, is discretized into non-overlapping elements or finite volumes. The partial differential equations are then discretized/transformed into algebraic equations by integrating
them over each discrete element. The system of algebraic equations is then solved to compute the values of the dependent variable for each of the elements.
In the finite volume method, some of the terms in the conservation equation are turned into face fluxes and evaluated at the finite volume faces. Because the flux entering a given volume is identical to that leaving the adjacent volume, the FVM is strictly conservative. This inherent conservation property of the FVM makes it the preferred method in CFD. Another important attribute of the FVM is that it can be formulated in the physical space on unstructured polygonal meshes. Finally in the FVM it is quite easy to implement a variety of boundary conditions in a noninvasive manner, since the unknown variables are evaluated at the centroids of the volume elements, not at their boundary faces.
These characteristics have made the Finite Volume Method quite suitable for the numerical simulation of a variety of applications involving fluid flow and heat and mass transfer, and developments in the method have been closely entwined with advances in CFD. From a limited potential at inception confined to solving simple physics and geometry over structured grids, the FVM is now capable of dealing with all kinds of complex physics and applications.
