Behaviour of Finite Difference Schemes for Advection Diffusion Equations

Research Report MRR96-062

Behaviour of Finite Difference Schemes for Advection Diffusion Equations

Chris Zoppou and Stephen Roberts

Abstract: All finite difference equations have an equivalent partial differential equation which is the actual partial differential equation being solved. The equivalent modified partial differential equation will not be identical to the original equation being modelled. It will generally contain additional higher-order spatial terms introduced by the finite difference approximation. The behaviour of a finite difference scheme can be examined by considering the behaviour of the equivalent modified partial differential equation. Analytical solutions are given for the equivalent modified partial differential equations for first, second and third-order finite difference schemes used to solve the advection equation. These analytical solutions are used to establish the accuracy of these schemes for the simulation of problems containing discontinuous profile

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