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基于三角形有限覆盖数值流形理论,提出了裂隙岩体二维不稳定温度场求解的数值流形方法(NMM),并推导了第一类温度边界条件处理的罚方法,给出了计算格式。数值流形方法采用两套覆盖,其中数学覆盖独立于求解区域,生成数学覆盖时不用考虑裂隙数量、位置和方向,避免了常规方法处理裂隙处网格划分的不便。对于裂隙岩体,裂隙两侧对应不同流形单元,可以实现温度的不连续模拟。裂隙作为内部流形单元或外部边界条件叠加进入到温度场的总体求解矩阵中,实现了裂隙岩体温度场的数值流形求解。该方法具有较高精度,且能求解任意多条裂隙的岩体温度场问题。最后对部分文献算例进行计算,结果具有较好的一致性。
Based on the numerical manifold theory of triangular finite coverage, a numerical manifold method (NMM) for solving the two-dimensional unstable temperature field of fractured rock mass was proposed. The penalty method for the first type of temperature boundary conditions was derived and the calculation format was given. The numerical manifold method uses two sets of coverings, of which math coverage is independent of the solution area. When generating math coverage, the number, position and orientation of the cracks are not considered, which avoids the inconvenience of conventional methods for meshing the cracks. For fractured rock mass, the two sides of fractures correspond to different manifold units, so that the discontinuity of temperature can be simulated. The fractures are added into the overall solution matrix of the temperature field as internal manifold units or external boundary conditions to solve the numerical manifold of temperature field of fractured rock mass. The method has high accuracy and can solve the rock mass temperature field problem with any number of fractures. Finally, the calculation of some literature examples, the results have a good consistency.