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A numerical treatment of the coupled viscous Burgers’ equation in the presence of very large Reynolds number

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  • Başhan, Ali

Abstract

A numerical investigation of the coupled viscous Burgers’ equation for very large Reynolds numbers do not exist in the literature. Coupled viscous Burgers’ equations are solved numerically in the presence of very large Reynolds numbers. For this case, numerical approach to the coupled viscous Burgers’ equation via contributions of two effective methods is used. The first component of the mixed method is finite difference method and the second one is differential quadrature method. For this process, the third order modified cubic B-spline functions are used as base function. To display the effectiveness of the present mixed method four different test problems have been investigated. For various values of the coefficients, more particularly for very large Reynolds numbers, in other words, for the very small value of kinematic viscosity parameters solutions are obtained. Error norms are calculated and compared with analytical results and also with numerical results of the related literature. Present results display that the present mixed method obtains high accurate solutions and in compatibility with both of the analytical and numerical results.

Suggested Citation

  • Başhan, Ali, 2020. "A numerical treatment of the coupled viscous Burgers’ equation in the presence of very large Reynolds number," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    • Handle: RePEc:eee:phsmap:v:545:y:2020:i:c:s0378437119320928
    DOI: 10.1016/j.physa.2019.123755
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    References listed on IDEAS

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    1. Li, Qianhuan & Chai, Zhenhua & Shi, Baochang, 2015. "A novel lattice Boltzmann model for the coupled viscous Burgers’ equations," Applied Mathematics and Computation, Elsevier, vol. 250(C), pages 948-957.
    2. Lai, Huilin & Ma, Changfeng, 2014. "A new lattice Boltzmann model for solving the coupled viscous Burgers’ equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 395(C), pages 445-457.
    3. Soliman, A.A., 2006. "The modified extended tanh-function method for solving Burgers-type equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 361(2), pages 394-404.
    4. Ali Başhan & N. Murat Yağmurlu & Yusuf Uçar & Alaattin Esen, 2018. "A new perspective for the numerical solutions of the cmKdV equation via modified cubic B-spline differential quadrature method," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 29(06), pages 1-17, June.
    5. Doğan Kaya, 2001. "An explicit solution of coupled viscous Burgers' equation by the decomposition method," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 27, pages 1-6, January.
    6. Mohanty, R.K. & Dai, Weizhong & Han, Fei, 2015. "Compact operator method of accuracy two in time and four in space for the numerical solution of coupled viscous Burgers’ equations," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 381-393.
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