Higher‐order boundary element methods for transient diffusion problems. Part I: Bounded flux formulation
Higher‐order boundary element methods for transient diffusion problems. Part I: Bounded flux formulation
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瞬态扩散问题的高阶边界元方法第一部分：有界通量公式。
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通讯作者：
G. Dargush
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作者：
M. Grigoriev;G. Dargush
尽管有大量关于热扩散时间相关问题的边界元方法(BEM)的出版物，但仍然存在需要解决的问题，最重要的是数值模拟的准确性。虽然对于稳态问题非常精确，但应用于暂态问题的常见边界元方法并不能产生高精度的数值解。本文研究了温度连续、热流有界的瞬变热扩散问题不能达到较高精度的原因。为了大大增强常用的边界元公式，我们提出了高阶时间内插函数，包括二次逼近和四次逼近。我们表明，高阶时间函数的使用大大减少了集中在拐角区域的数值误差，并且对于期望均匀分布的问题，得到了很好的沿边界的通量和温度分布的一致性。
Despite the significant number of publications on boundary element methods (BEM) for time‐dependent problems of heat diffusion, there still remain issues that need to be addressed, most importantly accuracy of the numerical modelling. Although very precise for steady‐state problems, the common boundary element methods applied to transient problems do not yield highly accurate numerical solutions. This paper investigates the reasons that prohibit achievement of a high level of accuracy for transient heat diffusion problems with continuous temperature and bounded heat flux solutions. In order to greatly enhance the commonly used boundary element formulations, we propose higher‐order time interpolation functions, including quadratic and quartic approximations. We show that the use of higher‐order time functions greatly reduces the numerical error concentrated in the corner regions, and results in very good uniformity of the flux and temperature distributions along the boundaries for problems where uniform distributions are expected.