基于时空广义有限差分法的制动器传热分析
Heat Transfer Analysis of Brakes Based on Spatio-temporal Generalized Finite Difference Method
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摘要: 基于时空联合技术, 发展一种时空广义有限差分法(ST-GFDM), 用于制动器传热分析。该方法直接对瞬态热传导问题进行离散, 避免了耗时耗力的时间差分过程和复杂结构的网格划分。通过典型数值算例验证方法的精度和有效性, 针对二维制动器简化模型和三维制动器模型进行瞬态传热模拟, 并与COMSOL Multiphysics软件的结果进行了比较。该算法具有二阶收敛性, 且能够在较少节点数条件下获得与有限元软件计算结果相近的精度。该方法不仅具有无须网格划分和数值积分等优点, 还克服了全局无网格配点法计算量大且矩阵病态的问题, 在制动器传热分析领域具有广泛应用前景。Abstract: This paper develops a spatio-temporal generalized finite difference method (ST-GFDM) based on spatio-temporal joint technology for brake thermal analysis. The proposed method directly discretizes transient heat transfer problems, avoiding the time-consuming and labor-intensive processes and complex mesh generation tasks. The accuracy and effectiveness of the method are validated through typical several numerical examples. Transient thermal simulations are conducted for simplified two-dimensional brake model and three-dimensional brake model, and the results are compared with those obtained from COMSOL Multiphysics. Numerical experiments demonstrate that the proposed algorithm achieves second-order convergence and maintains accuracy comparable to that of finite element software, even under conditions with fewer nodes. The developed method not only eliminates the need for meshing and numerical integration but also effectively addresses the challenges of high computational cost and matrix ill-conditioning inherent in global mesh-free collocation methods. These features highlight its broad potential for applications in brake heat transfer analysis.
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