Critique on “Volume penalization for inhomogeneous Neumann boundary conditions modeling scalar flux in complicated geometry”
Critique on “Volume penalization for inhomogeneous Neumann boundary conditions modeling scalar flux in complicated geometry”
复制标题
对“复杂几何中标量通量建模的非均匀诺依曼边界条件的体积惩罚”的批判
DOI：
10.1016/j.jcp.2021.110163
复制
发表时间：
2021
影响因子：
4.1
通讯作者：
Bhalla, Amneet Pal
中科院分区：
文献类型：
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作者：
Thirumalaisamy, Ramakrishnan;Nangia, Nishant;Bhalla, Amneet Pal
在过去的几十年里，复杂域内多物理场问题的数值模拟引起了人们的极大兴趣。在Angot等人的开创性工作中，作者描述了一种简单的方法，通过在控制方程中应用额外的强迫项来模拟不可压缩的气流。在[1]中，采用体积惩罚（VP）方法（也称为Brinkman惩罚方法）在障碍物界面处施加无滑移的Dirichlet边界条件。由于其表述和实现简单，VP技术已成功应用于多种流固耦合问题的研究，包括但不限于水的进出[2]、波能转换[3]、[4]、水生运动[5]、[6]、扑动不稳定性[7]、昆虫的扑动飞行[8]、[9]等。在所有这些应用中，都使用了VP方法的Dirichlet边界条件公式。在过去的几年里，已经提出了Neumann和更一般的Robin边界条件的惩罚方法，尽管对这些技术的分析仍然是一个活跃的研究领域[10]，[11],[12],[13],[14]。Kadoch et al.[10]扩展了Angot et al.[1]的Dirichlet边界条件VP公式，以允许施加齐次诺伊曼边界条件。在基于虚拟域方法的分布式拉格朗日乘子的独立背景下，Doostmohammadi等人（[15]）非正式地描述了一种通过简单地将障碍物内的导热系数设置为零来在界面上强制执行均匀通量边界条件的方法。Sakurai et al.[14]最近开发了一种基于流量的VP框架，用于在惩罚区域的边界上施加非均匀的、空间恒定的Neumann边界条件，该框架正式扩展了Kadoch et al.[14]的方法。这个扩展可以在VP框架内模拟更复杂的问题，例如不规则域中的通量驱动热对流。Sakurai等人基于通量的VP方法，修改了控制方程的扩散系数，在界面附近加入了一个附加的强迫项，以便在边界上施加期望的通量值。这提供了一种简单而有效的方法来对嵌入界面施加通量边界条件。
Numerical simulation of multiphysics problems within complex domains has garnered much interest in the past couple of decades. In the seminal work by Angot et al.[1], the authors describe a simple approach for simulating the incompressible flow over obstacles by applying an additional forcing term to the governing equations. In [1], this volume penalization (VP) methodology (also known as the Brinkman penalization method) was used to impose no-slip Dirichlet boundary conditions at the obstacle interface. Due to the simplicity of its formulation and implementation, the VP technique has been successfully applied to study a variety of fluid-structure interaction problems, including but not limited to water entry/exit [2], wave energy conversion [3],[4], aquatic locomotion [5],[6], fluttering instabilities [7], and flapping flight of insects [8],[9]. In all of these applications, the Dirichlet boundary condition formulation of the VP method was used. In the past few years penalization methods for Neumann and more general Robin boundary conditions have been proposed, although the analysis of such techniques is still an active area of research [10],[11],[12],[13],[14].Kadoch et al.[10] extended the Dirichlet boundary condition VP formulation of Angot et al.[1] to allow for the imposition of homogeneous Neumann boundary conditions. Independently within the context of distributed Lagrange multipliers based fictitious domain method, Doostmohammadi et al.[15] informally described a way to enforce homogeneous flux boundary conditions on an interface by simply setting the thermal conductivity to zero within the obstacle. Sakurai et al.[14] recently developed a flux-based VP framework for imposing inhomogeneous, spatially constant Neumann boundary conditions on the boundary of a penalization region, which formally extended the methodology of Kadoch et al.[10]. This extension enables the simulation of more complex problems within the VP framework, such as flux-driven thermal convection in irregular domains. In the flux-based VP approach of Sakurai et al., the diffusion coefficient of the governing equation is modified and an additional forcing term is applied near the interface in order to impose the desired flux value on the boundary. This provides a simple and efficient way to impose flux boundary conditions on embedded interfaces.