Piecewise–Analytical, Cell–Centered, Finite–Volume Methods for Multidimensional Advection–Reaction–Diffusion Equations

Cell–centered, finite–volume methods based on time discretization and linearization and approximate factorization techniques together with piecewise–linearization in space and piecewise–analytical integration, are presented and applied to a system of two–dimensional, nonlinear, advection–reaction–diffusion equations. The methods are exact for time–independent, one–dimensional, advection–diffusion equations with constant coefficients, are of the exponential–type, and one of them results in the well–known first–order upwind and second–order central–difference methods for very large and small Péclet numbers, respectively.