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Novel immersed boundary methods for thermal flow problems

机译：解决热流问题的新型浸入边界方法

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Purpose - The purpose of this paper is to present two efficient immersed boundary methods (IBM) for simulation of thermal flow problems. One method is for given temperature condition (Dirichlet type), while the other is for given heat flux condition (Neumann type). The methods are applied to simulate natural and mixed convection problems to check their performance. The comparison of present results with available data in the literature shows that the present methods can obtain accurate numerical results efficiently. Design/methodology/approach - The paper presents two efficient IBM solvers, in which the effect of thermal boundary to its surrounding fluid is considered through the introduction of a heat source/sink term into the energy equation. One is the temperature correction-based IBM developed for problems with given temperature on the wall. The other is heat flux correction-based IBM for problems with given heat flux on the wall. Note that in this solver, the offset of derivative condition is directly used to correct the temperature field. Findings - As compared with existing solvers, the temperature correction-based IBM determines the heat source/sink implicitly instead of pre-calculated explicitly, so that the boundary condition for temperature is accurately satisfied. To the best of the authors' knowledge, the work of heat flux correction-based IBM is the first endeavour for application of IBM to solve thermal flow problems with Neumann (heat flux) boundary condition. It was found that both methods presented in this work can efficiently obtain accurate numerical results for thermal flow problems. Originality/value - The two methods presented in this paper are novel. They can effectively solve thermal flow problems with Dirichlet and Neumann boundary conditions.
机译：目的-本文的目的是提出两种用于模拟热流问题的有效浸入边界方法（IBM）。一种方法用于给定的温度条件（Dirichlet类型），另一种方法用于给定的热通量条件（Neumann类型）。该方法用于模拟自然对流和混合对流问题，以检查其性能。现有结果与文献中现有数据的比较表明，本方法可以有效地获得准确的数值结果。设计/方法/方法-本文介绍了两种有效的IBM求解器，其中通过将热源/吸收项引入能量方程中来考虑热边界对其周围流体的影响。一种是基于温度校正的IBM，它针对墙壁上给定温度的问题而开发。另一个是基于热通量校正的IBM，用于解决壁上给定热通量的问题。请注意，在此求解器中，导数条件的偏移量直接用于校正温度场。发现-与现有求解器相比，基于温度校正的IBM隐式确定热源/散热器，而不是显式地预先计算，因此可以精确满足温度的边界条件。据作者所知，基于热通量校正的IBM的工作是应用IBM解决具有Neumann（热通量）边界条件的热流问题的第一项努力。发现在这项工作中提出的两种方法都可以有效地获得关于热流问题的精确数值结果。创意/价值-本文介绍的两种方法都很新颖。它们可以有效地解决Dirichlet和Neumann边界条件下的热流问题。

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