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A novel local meshless collocation method with partial upwind scheme for solving convection-dominated diffusion problems

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Abstract

In this study, a novel upwind local backward substitution method (upwind-BSM) is developed for the simulation of two-dimensional convection-dominated diffusion problems. The high-order Pascal polynomial expansion method with a characteristic length factor is adopted to approximate the known boundary condition for transforming the original problem into a problem with a homogeneous boundary condition. Then the transformed problem is solved by the radial basis function-finite difference method, which generates a sparse interpolation matrix to improve the computation efficiency and avoid the ill-conditioned problem of the traditional global backward substitution method. A partial upwind point-taking scheme is introduced to eliminate the numerical oscillation resulting from the convection term in the governing equation. Several numerical examples are considered to illustrate the accuracy and efficiency of the newly proposed method. The results demonstrate that the proposed local collocation method is an accurate, efficient, and oscillation-free method for the two-dimensional convection-dominated diffusion problems.

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Acknowledgements

The work described in this paper was supported by the National Key Research and Development Program of China (No. 2021YFB2600700), the National Natural Science Foundation of China (No. 52171272), the Significant Science and Technology Project of the Ministry of Water Resources of China (No. SKS-2022112), the Nan**g Water Science and Technology Project (No. 202203), and the 333 Talent Project of Training and Support in Key Industries.

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Authors and Affiliations

  1. Key Laboratory of Coastal Disaster and Defence (Ministry of Education), College of Mechanics and Materials, Hohai University, Nan**g, 211100, China

    Yuhui Zhang & Ji Lin

  2. A. Pidhornyi Institute of Mechanical Engineering Problems of NAS of Ukraine, 2/10 Pozharsky Street, Kharkiv, 61046, Ukraine

    Sergiy Reutskiy

  3. Institute of Structural Mechanics, Bauhaus-Universiat Weimar, 99423, Weimar, Germany

    Timon Rabczuk

  4. Nan**g Hydraulic Research Institute, Nan**g, 210029, China

    Jun Lu

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  1. Yuhui Zhang
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Correspondence to Ji Lin.

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Zhang, Y., Lin, J., Reutskiy, S. et al. A novel local meshless collocation method with partial upwind scheme for solving convection-dominated diffusion problems. Engineering with Computers (2024). https://doi.org/10.1007/s00366-024-02005-y

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