Boundary condition-enforced immersed boundary method for thermal flow problems with Dirichlet temperature condition and its applications
Boundary condition-enforced immersed boundary method for thermal flow problems with Dirichlet temperature condition and its applications
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DOI：
10.1016/j.compfluid.2011.12.006
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发表时间：
2012-03
影响因子：
2.8
通讯作者：
W. Ren;C. Shu;Jie Wu;Wenming Yang
中科院分区：
文献类型：
--
作者：
W. Ren;C. Shu;Jie Wu;Wenming Yang
本文提出了一种边界条件强制浸没边界方法，用于模拟具有Dirichlet型边界条件的自由对流和强迫对流问题。在能量方程中引入热源/热汇来模拟浸没边界的影响。与以往的工作不同，本文不是预先计算热源/热汇，而是隐式确定热源/热汇，使得由修正后的温度场内插的浸没边界上的温度准确地满足热条件。该方法的主要优点在于概念简单、易于实现和稳定性强。本文的另一个重要贡献是给出了两种计算平均Nusselt数的有效方法。它们基于欧拉点的温度修正和拉格朗日点的热通量，其中不需要温度梯度的近似。对强迫对流和自然对流问题进行了数值实验，验证了该方法的有效性，并提出了两种计算平均Nusselt数的方法。已经与文献中的现有数据达成了良好的一致。
A boundary condition-enforced immersed boundary method is presented in this paper for simulation of free and forced convection problems with Dirichlet-type boundary condition. The heat source/sink is introduced into the energy equation to model the effect of immersed boundary. Different from previous works, in this paper, the heat source/sink is not pre-calculated, but determined implicitly in such a way that temperature at the immersed boundary interpolated from the corrected temperature field accurately satisfies the thermal condition. The main advantage of the proposed method lies in its simple concept, easy implementation and robustness in stability. Another important contribution of the paper is that it presents two efficient ways to calculate the average Nusselt number. They are based on temperature correction at Eulerian points and heat flux at Lagrangian points, in which no approximation for temperature gradients is needed. Numerical experiments for both forced convection and natural convection problems have been conducted to validate the capability and efficiency of the present method and proposed two ways to calculate the average Nusselt number. Good agreements with available data in the literature have been achieved.