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A Linearized High-Order Combined Compact Difference Scheme for Multi-Dimensional Coupled Burgers' Equations

A Linearized High-Order Combined Compact Difference Scheme for Multi-Dimensional Coupled Burgers' Equations
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Year:    2018

Numerical Mathematics: Theory, Methods and Applications, Vol. 11 (2018), Iss. 2 : pp. 299–320

Abstract

Multi-dimensional coupled Burgers' equations are important nonlinear partial differential equations arising in fluid mechanics. Developing high-order and efficient numerical methods for solving the Burgers' equation is essential in many real applications since exact solutions can not be obtained generally. In this paper, we seek a high-order accurate and efficient numerical method for solving multi-dimensional coupled Burgers' equations. A linearized combined compact difference (CCD) method together with alternating direction implicit (ADI) method is proposed. The CCD-ADI method is sixth-order accuracy in space variable and second-order accuracy in time variable. The resulting linear system at each ADI computation step corresponds to a block-tridiagonal system which can be effectively solved by the block Thomas algorithm. Fourier analysis shows that the method is unconditionally stable. Numerical experiments including both two-dimensional and three-dimensional problems are conducted to demonstrate the accuracy and efficiency of the method.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/nmtma.OA-2017-0090

Numerical Mathematics: Theory, Methods and Applications, Vol. 11 (2018), Iss. 2 : pp. 299–320

Published online:    2018-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    22

Keywords:   

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