A Linearized High-Order Combined Compact Difference Scheme for Multi-Dimensional Coupled Burgers' Equations
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.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
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