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Conservative characteristic finite difference method based on ENO and WENO interpolation for 2D convection–diffusion equations

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Abstract

In the paper, the space second-order conservative characteristic finite difference method based on essentially non-oscillatory (ENO) and weighted essentially non-oscillatory (WENO) interpolation for solving two-dimensional conservative convection–diffusion equations in divergence form is developed. Combining the splitting technique, characteristic difference and mass correction method, a two-dimensional convection–diffusion equations are changed into the two-dimensional parabolic equations, where the convection term and unsteady term are considered as one term. The solutions and fluxes on the staggered meshes are computed by the splitting implicit solution-flux coupled scheme. Numerical experiments are presented to illustrate mass conservation and convergence.

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Acknowledgements

The authors would thank referees for their comments and suggestions on their manuscript which have helped to improve the paper.

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Authors and Affiliations

  1. School of Mathematics, Shandong University, Jinan, Shandong, 250100, China

    Tongtong Hang, Yuxiao Zhai, Zhongguo Zhou & Wenjun Zhao

  2. School of Information Science and Engineering, Shandong Agricultural University, Taian, Shandong, 271018, China

    Tongtong Hang

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  1. Tongtong Hang
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  2. Yuxiao Zhai
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  3. Zhongguo Zhou
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  4. Wenjun Zhao
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Correspondence to Zhongguo Zhou.

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Communicated by Abdellah Hadjadj.

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This work was supported partially by the National Natural Science Foundation of China (Grant No. 61703250) and Shandong Agricultural University (Grant No. xxxy201704). Tongtong Hang and Yuxiao Zhai are co-first authors of the article .

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Hang, T., Zhai, Y., Zhou, Z. et al. Conservative characteristic finite difference method based on ENO and WENO interpolation for 2D convection–diffusion equations. Comp. Appl. Math. 40, 202 (2021). https://doi.org/10.1007/s40314-021-01594-4

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  • DOI: https://doi.org/10.1007/s40314-021-01594-4

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