Finite Volume Methods
The finite volume (FV) method is described for the generic scalar transport equation in this chapter, including the approximation of surface and volume integrals and the use of interpolation to obtain variable values and derivatives at locations other than cell centers. Development of higher-order schemes and simplification of the resulting algebraic equations using the deferred-correction approach is also described. Special attention is paid to the analysis of discretization errors caused by interpolation and integral approximations. Finally, implementation of the various boundary conditions is discussed. The chapter closes with application of some of the basic methods to several examples using Cartesian grids.