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A high-order compact Hermite difference method for two-dimensional double-diffusive convection

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  • Yang, Jianqing
  • Qiu, Jianxian

Abstract

In this paper, a class of high-order compact Hermite scheme is presented for the simulation of double-diffusive convection. To maintain stability, the convective fluxes are split into positive and negative parts, then the upwind compact Hermite difference methods are used to discretize the positive and negative fluxes, respectively. The diffusion fluxes of the governing equations are directly approximated by a high-order finite difference scheme based on the Hermite interpolation. A key advantage of the proposed schemes is that the solution derivatives are directly obtained from the compact central difference scheme, eliminating the need for auxiliary derivative equation. The third-order Runge-Kutta method is utilized for the temporal discretization. Several numerical tests are presented to assess the numerical capability of the newly proposed algorithm. The numerical results are in great agreement with the benchmark solutions and some of the accurate results available in the literature. Subsequently, we apply the algorithm to solve steady and unsteady problems of double-diffusive convection and a preliminary application to the double-diffusive convection for different Raleigh numbers and aspect ratios is carried out.

Suggested Citation

  • Yang, Jianqing & Qiu, Jianxian, 2026. "A high-order compact Hermite difference method for two-dimensional double-diffusive convection," Applied Mathematics and Computation, Elsevier, vol. 528(C).
    • Handle: RePEc:eee:apmaco:v:528:y:2026:i:c:s0096300326001888
    DOI: 10.1016/j.amc.2026.130136
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