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Numerical simulation for 2D double-diffusive convection (DDC) in rectangular enclosures based on a high resolution upwind compact streamfunction model I: numerical method and code validation

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Abstract

A high resolution upwind compact streamfunction numerical algorithm for two-dimensional (2D) double-diffusive convection (DDC) is developed. The unsteady Navier-Stokes (N-S) equations in the streamfunction-velocity form and the scalar temperature and concentration equations are used. An optimized third-order upwind compact (UCD3_opt) scheme with a low dispersion error for the first derivatives is utilized to approximate the third derivatives of the streamfunction in the advection terms of the N-S equations and the first derivatives in the advection terms of the scalar temperature and concentration equations. The remaining first derivatives of the streamfunction (velocity), temperature, and concentration variables used in the governing equations are discretized by the fourth-order compact Padé (SCD4) schemes. With the temperature and concentration variables and their approximate values of the first derivatives obtained by the SCD4 schemes, the explicit fourth-order compact schemes are suggested to approximate the second derivatives of temperature and concentration in the diffusion terms of the energy and concentration equations. The discretization of the temporal term is executed with the second-order Crank-Nicolson (C-N) scheme. To assess the spatial behavior capability of the established numerical algorithm and verify the developed computer code, the DDC flow is numerically solved. The obtained results agree well with the benchmark solutions and some accurate results available in the literature, verifying the accuracy, effectiveness, and robustness of the provided algorithm. Finally, a preliminary application of the proposed method to the DDC is carried out.

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Authors and Affiliations

  1. Institute of Mechanics and Computational Engineering, Department of Aeronautics and Astronautics, Fudan University, Shanghai, 200433, China

    Yaping Yan, Shuang Wu & Zhenfu Tian

  2. College of Science, Liaoning Technical University, Fuxin, Liaoning Province, 123000, China

    Yaping Yan

  3. Research Institute of Intelligent Complex Systems, Fudan University, Shanghai, 200433, China

    Kaiyuan Tian & Zhenfu Tian

  4. School of Life Sciences, Fudan University, Shanghai, 200433, China

    Kaiyuan Tian

Authors
  1. Yaping Yan
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  2. Shuang Wu
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  4. Zhenfu Tian
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Correspondence to Zhenfu Tian.

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Citation: YAN, Y. P., WU, S., TIAN, K. Y., and TIAN, Z. F. Numerical simulation for 2D double-diffusive convection (DDC) in rectangular enclosures based on a high resolution upwind compact streamfunction model I: numerical method and code validation. Applied Mathematics and Mechanics (English Edition), 43(9), 1431–1448 (2022) https://doi.org/10.1007/s10483-022-2895-6

Project supported by the National Natural Science Foundation of China (Nos. 11872151, 11372075, and 91330112)

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Yan, Y., Wu, S., Tian, K. et al. Numerical simulation for 2D double-diffusive convection (DDC) in rectangular enclosures based on a high resolution upwind compact streamfunction model I: numerical method and code validation. Appl. Math. Mech.-Engl. Ed. 43, 1431–1448 (2022). https://doi.org/10.1007/s10483-022-2895-6

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  • DOI: https://doi.org/10.1007/s10483-022-2895-6

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