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Truncation errors of selected finite-difference methods for two-dimensional advection-diffusion equation with mixed derivatives

Kalinowska M.B., Rowiński P.M.

Acta Geophysica

2007

Vol. 55, no. 1

107-118

The spread of a passive contaminant in an open-channel reach is considered with use of a two-dimensional advection-diffusion equation with the included offdiagonal dispersion coefficients. This paper presents the calculation of truncation errors, namely numerical diffusion and numerical dispersion for various finite difference schemes. The accuracy of the considered finite-difference approximations is analysed by deriving and studying the relevant modified partial differential equation.

Numeryczne rozwiązywanie dwuwymiarowego równania przenoszenia masy w rzekach

Kalinowska M.

Przegląd Naukowy Inżynieria i Kształtowanie Środowiska

2006

Vol. 15, No. 1

13--20

The transport processes in rivers in many cases can be represented by depth-averaged, two-dimensional advection-diffusion equation. The equation with general boundary and initial conditions does not have an exact analytical solution, and therefore problem requires numerieal methods. It is important to choose an algorithm, which is accurate, stable and fast. The Altemating Direction Implicit method has been proposed to solve the problem. The scheme is stable and relatively fast. Tests in a simple canal for which the analytical solution is known, show that the scheme can give us an accurate solution comparing to the analytical one.