HIGH ORDER COMPACT METHOD USING EXPONENTIAL DIFFERENCE SCHEMES IN THE SOLUTION OF THE CONVECTIVE DIFFUSION EQUATION

Resumo

We will present in this paper scheme for the numerical solution of the convective-diffusive

equations in incompressible, inviscid, stationary and transient flows by the technique known as High-
Order Exponential Finite Difference Schema. Today, it is generally accepted that a realities arise in the

various branches of science, such as physics, biology, chemistry, materials, engineering, ecology, bio-
mechanical economics, combustion, computer science, epidemiology, finance, groundwater pollution,

heat transfer, neurosciences, physiology, infiltration flow, solids mechanics, and turbulence are modeled
by EDP typically similar to the RDC equation - Reaction-Diffusion-Convection Equation. In the last
decades, many known numerical techniques have been applied to solve this problem. RDC equation:
finite differences, finite volumes, finite elements and spectral or meshless, to name a few.
In this respect, a general-purpose numerical methodology still does not seem to be available actually.
In general, the methods cited are successful when convection, reaction or combination of both acting

together are largely dominated by diffusion, tending to purely diffusive process. The situation is drasti-
cally altered when convection, reaction, or a combination of both overload diffusion. In such situations,

numerical instability arises in cases where diffusion becomes less predominant. Thus, the purpose of this
paper is to present the above scheme.