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Modified Equation Approach Applied to 2D Advection-Diffusion Equation with Mixed Derivatives

Author(s): Monika B. Kalinowska; Pawel M. Rowinski

Linked Author(s): Monika Kalinowska, Pawel M. Rowinski

Keywords: No Keywords

Abstract: Solution of full mass transport equations in their two-dimensional version requires the use of numerical schemes. The root of finite-difference schemes is a Taylor expansion. Since it is impossible to compute all the terms in an infinite series, a numerical scheme necessarily uses a truncated series. So far most of the studies aimed at the evaluation of numerical errors associated with the finite-difference solutions of mass transport equations were either devoted to 1D cases or in case of2D transport processes – they were usually restricted to the simple case in which mixed derivatives were avoided. The method of the present study pertains to the so-called Modified Equation Approach. The modified equation is derived by first expanding each term of the applied difference scheme in a Taylor series and then eliminating time derivatives higher than the first-order by specially designed mathematical manipulations. Modified Equation has been created for a number of finite difference schemes that might be applied to advection-diffusion equation with mixed derivatives and expressions for the errors of numerical diffusion and dispersion are derived and compared for different schemes.


Year: 2009

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