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A fifth-order finite volume weighted compact scheme for solving one-dimensional Burgers’ equation

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  • Guo, Yan
  • Shi, Yu-feng
  • Li, Yi-min

Abstract

In the present paper, a high-order finite volume compact scheme is proposed to solve one dimensional Burgers’ equation. The nonlinear advective terms are computed by the fifth-order finite volume weighted upwind compact scheme, in which the nonlinear weighted essentially non-oscillatory weights are coupled with lower order compact stencils. The diffusive terms are discretized by using the finite volume six-order Padé scheme. The strong stability preserving third-order Runge–Kutta time discretizations is used in this work. Numerical results are compared with the exact and some existing numerical solutions to demonstrate the essentially non-oscillatory and high resolution of the proposed method. The numerical results are shown to be more accurate than some numerical results given in the literature.

Suggested Citation

  • Guo, Yan & Shi, Yu-feng & Li, Yi-min, 2016. "A fifth-order finite volume weighted compact scheme for solving one-dimensional Burgers’ equation," Applied Mathematics and Computation, Elsevier, vol. 281(C), pages 172-185.
    • Handle: RePEc:eee:apmaco:v:281:y:2016:i:c:p:172-185
    DOI: 10.1016/j.amc.2016.01.061
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    References listed on IDEAS

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    1. Mukundan, Vijitha & Awasthi, Ashish, 2015. "Efficient numerical techniques for Burgers’ equation," Applied Mathematics and Computation, Elsevier, vol. 262(C), pages 282-297.
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    Cited by:

    1. Cavoretto, Roberto, 2022. "Adaptive LOOCV-based kernel methods for solving time-dependent BVPs," Applied Mathematics and Computation, Elsevier, vol. 429(C).
    2. Li, Wenjuan & Gao, Fuzheng & Cui, Jintao, 2024. "A weak Galerkin finite element method for nonlinear convection-diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 461(C).
    3. Zhang, Xu & Jiang, Yanqun & Hu, Yinggang & Chen, Xun, 2022. "High-order implicit weighted compact nonlinear scheme for nonlinear coupled viscous Burgers’ equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 196(C), pages 151-165.
    4. Fu, Fangyan & Li, Jiao & Lin, Jun & Guan, Yanjin & Gao, Fuzheng & Zhang, Cunsheng & Chen, Liang, 2019. "Moving least squares particle hydrodynamics method for Burgers’ equation," Applied Mathematics and Computation, Elsevier, vol. 356(C), pages 362-378.
    5. Kaushik, Sonali & Kumar, Rajesh, 2023. "Optimized decomposition method for solving multi-dimensional Burgers’ equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 208(C), pages 326-350.

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