Volume 11, Issue 2
A Linearized High-Order Combined Compact Difference Scheme for Multi-Dimensional Coupled Burgers' Equations

Buyun Chen, Dongdong He & Kejia Pan

Numer. Math. Theor. Meth. Appl., 11 (2018), pp. 299-320.

Published online: 2018-11

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  • 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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@Article{NMTMA-11-299, author = {}, title = {A Linearized High-Order Combined Compact Difference Scheme for Multi-Dimensional Coupled Burgers' Equations}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2018}, volume = {11}, number = {2}, pages = {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.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2017-0090}, url = {http://global-sci.org/intro/article_detail/nmtma/12431.html} }
TY - JOUR T1 - A Linearized High-Order Combined Compact Difference Scheme for Multi-Dimensional Coupled Burgers' Equations JO - Numerical Mathematics: Theory, Methods and Applications VL - 2 SP - 299 EP - 320 PY - 2018 DA - 2018/11 SN - 11 DO - http://doi.org/10.4208/nmtma.OA-2017-0090 UR - https://global-sci.org/intro/article_detail/nmtma/12431.html KW - AB -

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.

Buyun Chen, Dongdong He & Kejia Pan. (2020). A Linearized High-Order Combined Compact Difference Scheme for Multi-Dimensional Coupled Burgers' Equations. Numerical Mathematics: Theory, Methods and Applications. 11 (2). 299-320. doi:10.4208/nmtma.OA-2017-0090
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