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An extension of the one‐dimensional von Rosenberg finite difference scheme to multidimensional problems of the convection dispersion equation
Author(s) -
ElAgeli Muktar Ali,
Chierici Gianluigi
Publication year - 1988
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.1690040102
Subject(s) - mathematics , dispersion (optics) , finite difference , dispersion relation , crank–nicolson method , mathematical analysis , constant (computer programming) , finite difference method , constant coefficients , physics , optics , computer science , programming language
The Crank Nicolson implicit form of the finite difference analogue of the convection‐dispersion equation does not yield stable solutions when the dispersion coefficient of the medium D is too small compared with the injected fluid velocity V —i.e, 0 < ( R = 2 D / V Δ X ) < 1. Von Rosenberg developed a simple, highly accurate and stable finite difference scheme for the one‐dimensional case of constant velocity and dispersion coefficient for 0 < R < 1. El‐Ageli extended von Rosenberg's method to the multilayered case of varying velocity and dispersion coefficient. This paper goes a step further and extends von Rosenberg's scheme to the linear multidimensional system with constant velocities and dispersion coeffcients when: 0 < ( R x , R y ,…,) < 1. When this new scheme is compared with the conventional Crank‐Nicolson method, it is found that even though there are some restrictions to the spacial grid spacings in relation to the time step, the computational effort is much less and the results obtained are stable.