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<p>This paper presents a pressure projection algorithm integrating the modular grad-div stabilization with the geometric average approximation, aiming to establish an efficient numerical algorithm for solving the two-domain natural convection coupling problem. The proposed algorithm is linear, decoupled, and unconditionally stable. Compared with the usual geometric average algorithm, the proposed algorithm separates the pressure term from the momentum equation and adds a grad-div stabilization term. It will not only avoid the numerical difficulty caused by the saddle-point problem, but also reduce divergence error and improve the computational efficiency. Moreover, the theoretical analysis demonstrates its unconditional stability, and some numerical experiments show its rationality and effectiveness.</p>

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A pressure projection algorithm based on the modular grad-div stabilization for the two-domain natural convection problem

  • 期刊论文

  • 发表日期：

    2026年2月4日

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  • Binchang Huo,
  • Pengzhan Huang

摘要

This paper presents a pressure projection algorithm integrating the modular grad-div stabilization with the geometric average approximation, aiming to establish an efficient numerical algorithm for solving the two-domain natural convection coupling problem. The proposed algorithm is linear, decoupled, and unconditionally stable. Compared with the usual geometric average algorithm, the proposed algorithm separates the pressure term from the momentum equation and adds a grad-div stabilization term. It will not only avoid the numerical difficulty caused by the saddle-point problem, but also reduce divergence error and improve the computational efficiency. Moreover, the theoretical analysis demonstrates its unconditional stability, and some numerical experiments show its rationality and effectiveness.