用有限元显式算法解具有烧蚀动边界的传热问题

A FINITE-ELEMENT EXPLICIT ALGORITHM SOLVINGTHE HEAT TRANSFER PROBLEMS WITHABLATION MOVING BOUNDARY

本文借助于运动坐标系用显式有限元算法求解烧蚀动边界的传热问题。通过坐标变换,在变换平面内确定固定的有限元结点,物理平面内对应的结点随边界的烧蚀而运动。在线性插值函数模式下温度的时间导数在三角形单元中处处相等的假设下导出有限元方程的显式计算格式。对横观各向同性材料的端头帽在再入飞行中的烧蚀和瞬时温度场的计算结果与用有限差分法计算的结果相互吻合。

An explicit finite element method is presented in this paper to solve the heat transfer problem with ablation moving boundary in a moving coordinate system. Through coordinate transformation, the element grids are fixed in the transformed plane, but movable in physi-cal plane as the boundary ablated. An explicit scheme for the finite element equation is established under an assumption that the derivatives of temperature with respect to time on all grids of each tringle element with linear interpolation are uniform.It is shown that the computationatl results on the ablated shape and the transient temperature fields of a reentry nosetip with crosswise iso-tropic material are almost identical to those obtained from the finite difference method.