Abstract In this paper, an efficient, unified finite difference method for imposing mixed Dirichlet, Neumann and Robin boundary conditions on irregular domains is proposed, leveraging on our previous work [Chai et al., J. Comput. Phys. 400 (2020): 108890]. The level set method is applied to describe the arbitrarily-shaped interface, and the ghost fluid method is utilized to address the complex discontinuities on the interface. The core of this method lies in providing required ghost values under the restriction of mixed boundary conditions, which is done in a fractional-step way. Specifically, the normal derivative is calculated in the concerned subdomain by aid of a linear polynomial reconstruction, then the normal derivative and the ghost value are successively extrapolated to the other subdomain using a linear partial differential equation approach. A series of Poisson problems with mixed boundary conditions and a heat transfer test are performed to validate the method, highlighting its convergence accuracy in the L1 and L∞ norms. The method produces second-order accurate solutions with first-order accurate gradients, and is easy to implement in multi-dimensional configurations. In summary, the method represents a promising tool for imposing mixed boundary conditions, which will be applied to practical problems in future work.

中文翻译：

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在基于水平集/鬼流体的有限差分框架中对不规则域施加混合 Dirichlet-Neumann-Robin 边界条件

摘要 在本文中，利用我们之前的工作 [Chai 等人，J. Comput. ]，提出了一种有效、统一的有限差分方法，用于在不规则域上施加混合 Dirichlet、Neumann 和 Robin 边界条件。物理。400 (2020): 108890]。水平集方法用于描述任意形状的界面，鬼流体方法用于解决界面上的复杂不连续性。该方法的核心在于在混合边界条件的限制下提供所需的鬼值，这是以分数步的方式完成的。具体来说，通过线性多项式重建在相关子域中计算正态导数，然后使用线性偏微分方程方法将法向导数和鬼值连续外推到另一个子域。执行一系列具有混合边界条件的泊松问题和传热测试来验证该方法，突出了其在 L1 和 L∞ 范数中的收敛精度。该方法产生具有一阶精确梯度的二阶精确解，并且易于在多维配置中实现。总之，该方法代表了一种施加混合边界条件的有前途的工具，它将在未来的工作中应用于实际问题。该方法产生具有一阶精确梯度的二阶精确解，并且易于在多维配置中实现。总之，该方法代表了施加混合边界条件的有前途的工具，它将在未来的工作中应用于实际问题。该方法产生具有一阶精确梯度的二阶精确解，并且易于在多维配置中实现。总之，该方法代表了一种施加混合边界条件的有前途的工具，它将在未来的工作中应用于实际问题。