研究裂隙岩体渗流传热问题对于地热能的开发有着重要意义。基于渗流传热耦合理论和有限差分法,给出了单裂隙岩体渗流传热问题的一种精细解法,包括以下步骤:首先依据傅立叶定律及能量守恒原理分别构建了裂隙与岩体的控制方程,随后,考虑到岩体与裂隙的不同物理性质,引入多重介质模型,并采用无厚度线单元模拟裂隙;通过有限差分理论将偏微分方程转换为常微分方程;最后借助精细积分法进行高精度求解,获得求解域内的温度场。与解析方法对比,验证了本文方法的有效性。算例1表明,相比传统有限元法,本文方法具有良好的稳定性。算例2中,举例阐述了不同参数对渗流传热的影响并进行了参数敏感度分析。最后,讨论分析了控制方程差分格式的稳定性条件。本文方法能够为研究裂隙岩体渗流传热问题提供参考。
The study of seepage heat-transfer coupling in single-fractured rock mass is critical for advancing geothermal energy development. Based on the coupled theory of seepage and heat transfer and finite difference method, a refined solution for the seepage and heat transfer problem of single fractured rock mass is proposed. The methodology comprises the following steps: First, governing equations for fractures and rock matrices are established based on Fourier's law and energy conservation principles. To account for the distinct physical properties of fractures and rock matrices, a multi-medium model is introduced, where fractures are represented using zero-thickness line elements. The partial differential equations are systematically discretized into ordinary differential equations via finite difference approximations. High-precision solutions for temperature field distributions are then obtained through the Precise Integration Method (PIM). Comparison with parsing methods confirms the method's accuracy. Numerical Case 1 demonstrates superior stability compared to conventional finite element methods, and this method has good stability. In Case 2, parametric influences on flow-heat transfer dynamics are systematically investigated, accompanied by a sensitivity analysis. Furthermore, stability criteria for the discretized governing equations are rigorously analyzed. Research has shown that the method proposed in this paper can provide a new numerical solution approach for the heat transfer problem of seepage in fractured rock masses.
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