边界节点法计算二维瞬态热传导问题

Boundary Knot Method for 2D Transient Heat Conduction Problems

采用边界节点法(BKM)结合双重互易法(DRM)求解二维瞬态热传导问题.采用差分格式处理时间变量,可将原瞬态热传导方程转化为一系列非齐次修正的Helmholtz方程.随后,方程的解可分为特解和齐次解两部分计算,引入双重互易法在区域内部配点求解方程的特解,采用边界节点法仅需边界配点求解方程的齐次解.给出的数值算例显示该方法计算精度高,适用性好,具有很好的稳定性和收敛性,适合求解瞬态热传导问题.

The boundary knot method （BKM） in conjunction with the dual reciprocity method （DRM） was introduced to solve 2D transient heat conduction problems. With the finite differ- ence scheme applied to deal with the time derivative term, the transient heat conduction equa- tion was converted to a set of nonhomogeneous modified Helmholtz equations. Then the numer- ical solution to the nonhomogeneous problems was divided into two parts： the particular solu- tion and the homogeneous solution. The DRM with few inner interpolation nodes was employed to get the particular solution, and the BKM with boundary-only nodes used to obtain the homo- geneous solution. Numerical results show that the present combined method has the merits of high accuracy, wide applicability, good stability and rapid convergence, which were appealing to solving transient heat conduction problems.