Volume 9, Issue 4
Exponential Compact Higher Order Scheme for Nonlinear Steady Convection-diffusion Equations

Y. V. S. S. Sanyasiraju & Nachiketa Mishra

Commun. Comput. Phys., 9 (2011), pp. 897-916.

Published online: 2011-09

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  • Abstract

This paper presents an exponential compact higher order scheme for Convection-Diffusion Equations (CDE) with variable and nonlinear convection coeffi- cients. The scheme is O(h 4 ) for one-dimensional problems and produces a tri-diagonal system of equations which can be solved efficiently using Thomas algorithm. For twodimensional problems, the scheme produces an O(h 4+k 4 ) accuracy over a compact nine point stencil which can be solved using any line iterative approach with alternate direction implicit procedure. The convergence of the iterative procedure is guaranteed as the coefficient matrix of the developed scheme satisfies the conditions required to be positive. Wave number analysis has been carried out to establish that the scheme is comparable in accuracy with spectral methods. The higher order accuracy and better rate of convergence of the developed scheme have been demonstrated by solving numerous model problems for one and two-dimensional CDE, where the solutions have the sharp gradient at the solution boundary.

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@Article{CiCP-9-897, author = {Y. V. S. S. Sanyasiraju and Nachiketa Mishra}, title = {Exponential Compact Higher Order Scheme for Nonlinear Steady Convection-diffusion Equations}, journal = {Communications in Computational Physics}, year = {2011}, volume = {9}, number = {4}, pages = {897--916}, abstract = {

This paper presents an exponential compact higher order scheme for Convection-Diffusion Equations (CDE) with variable and nonlinear convection coeffi- cients. The scheme is O(h 4 ) for one-dimensional problems and produces a tri-diagonal system of equations which can be solved efficiently using Thomas algorithm. For twodimensional problems, the scheme produces an O(h 4+k 4 ) accuracy over a compact nine point stencil which can be solved using any line iterative approach with alternate direction implicit procedure. The convergence of the iterative procedure is guaranteed as the coefficient matrix of the developed scheme satisfies the conditions required to be positive. Wave number analysis has been carried out to establish that the scheme is comparable in accuracy with spectral methods. The higher order accuracy and better rate of convergence of the developed scheme have been demonstrated by solving numerous model problems for one and two-dimensional CDE, where the solutions have the sharp gradient at the solution boundary.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.171209.300710a}, url = {http://global-sci.org/intro/article_detail/cicp/7527.html} }
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