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Non-uniform HOC Scheme for the 3D Convection–Diffusion Equation
Applied and Computational Mathematics
Volume 2, Issue 3, June 2013, Pages: 64-77
Received: May 13, 2013; Published: Jun. 30, 2013
Authors
Rabab Ahmed Shanab, Department of Engineering Mathematics, Faculty of Engineering, Zagazig University, Egypt
Laila Fouad Seddek, Department of Engineering Mathematics, Faculty of Engineering, Zagazig University, Egypt
Salwa Amin Mohamed, Department of Engineering Mathematics, Faculty of Engineering, Zagazig University, Egypt
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Abstract
In this paper, we extend the work of Kalita et al. [11] to solve the steady 3D convection-diffusion equation with variable coefficients on non-uniform grid. The approach is based on the use of Taylor series expansion, up to the fourth order terms, to approximate the derivatives appearing in the 3D convection diffusion equation. Then the original convection-diffusion equation is used again to replace the resulting higher order derivative terms. This leads to a higher order scheme on a compact stencil (HOC) of nineteen points. Effectiveness of this method is seen from the fact that it can handle the singularity perturbed problems by employing a flexible discretized grid that can be adapted to the singularity in the domain. Four difficult test cases are chosen to demonstrate the accuracy of the present scheme. Numerical results show that the fourth order accuracy is achieved even though the Reynolds number (Re) is high.
Keywords
3D Convection–Diffusion Equation; Variable Coefficient; Fourth Order Compact Scheme; Non-Uniform Grids; Algebraic Multigrid
Rabab Ahmed Shanab, Laila Fouad Seddek, Salwa Amin Mohamed, Non-uniform HOC Scheme for the 3D Convection–Diffusion Equation, Applied and Computational Mathematics. Vol. 2, No. 3, 2013, pp. 64-77. doi: 10.11648/j.acm.20130203.11
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