瞬态热传导问题的精细积分-双重互易边界元法

发布时间：2018-12-10 15:28

【摘要】：采用双重互易边界元法结合精细积分法求解二维含热源的瞬态热传导问题。针对边界积分方程中热源项和温度关于时间导数项引起的域积分,采用双重互易法处理,将域积分转换为边界积分。采用边界元法将边界积分方程离散后,得到关于时间的微分方程组,并利用精细积分法处理其中的指数型矩阵;对于微分方程组中由边界条件和热源项引起的非齐次项,采用解析的方法计算。为了比较精细积分-双重互易边界元法的计算效果,同时使用有限差分法计算温度对时间的导数项。通过数值算例验证了本文方法的有效性和精确性。计算结果表明:时间步长对于精细积分-双重互易边界元法的结果影响较小,而有限差分法对时间步长比较敏感且只在时间步长选取较小时有效;当选取较大时间步长时,精细积分-双重互易边界元法依然具有良好的计算精度。
[Abstract]:The dual reciprocal boundary element method and the precise integration method are used to solve the transient heat conduction problem of two dimensional heat source. For the domain integral caused by the heat source term and the time derivative term of temperature in the boundary integral equation, the domain integral is transformed into the boundary integral by using the double reciprocal method. After the boundary integral equation is discretized by the boundary element method, the system of differential equations about time is obtained, and the exponential matrix is treated by the precise integration method. The inhomogeneous terms caused by boundary conditions and heat source terms in differential equations are calculated by analytical method. In order to compare the computational effect of the precise integral-double reciprocal boundary element method, the derivative term of temperature to time is calculated by using the finite difference method. The effectiveness and accuracy of the proposed method are verified by numerical examples. The results show that the time step size has little effect on the results of the precise integral-dual reciprocal boundary element method, while the finite difference method is more sensitive to the time step size and is effective only when the time step size is small. When a large time step is selected, the precision integral-dual reciprocal boundary element method still has a good calculation accuracy.
【作者单位】：合肥工业大学土木与水利工程学院;
【基金】：国家自然科学基金(11672098;11502063) 安徽省自然科学基金(1608085QA07)
【分类号】：O241.8

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