Finite volume method for one-dimensional steady state diffusion
The Finite volume method in computational fluid dynamics is a discretization technique for partial differential equations that arise from physical conservation laws. These equations can be different in nature, e.g. elliptic, parabolic, or hyperbolic. The first well-documented use of this method was by Evans and Harlow (1957) at Los Alamos. The general equation for steady diffusion can be easily be derived from the general transport equation for property "Φ" by deleting transient and convective terms. General Transport equation can be defined as formula_1, where formula_2 is density and formula_3 is  the conserved quantity, formula_4 is the Diffusion coefficient and formula_5 is the Source term. formula_6 is the Net rate of flow of formula_3 out of fluid element (convection), formula_8 is Rate of increase of formula_3 due to diffusion, formula_10 is Rate of increase of formula_11 due to sources. formula_12 is Rate of increase of formula_3 of fluid element(transient), Conditions under which the transient and convective terms goes to zero: For one-dimensional, steady-state diffusion, General Transport equation reduces to: or, The following steps comprise the finite volume method for one-dimensional steady state diffusion - STEP 1 Grid Generation STEP  2 Discretization formula_20 , where formula_21 is Cross-sectional Area Cross section (geometry) of control volume face, formula_22 is Volume, formula_23is average value of source S over the control volume. formula_29 , formula_30. formula_34. formula_35. formula_36. formula_37 where STEP 3: Solution of equations This method can also be applied to a 2D situation. See Finite volume method for two dimensional diffusion problem.