迭代法求解航天器热网络方程的收敛条件与时间步长优化

热分析计算是航天器热设计验证和在轨温度预示的重要手段，其实质是对描述航天器在轨状态的能量平衡方程即热网络方程的求解。作为典型的非线性问题，航天器热网络方程通常采用迭代法求解，且目前尚无完善的理论可以判断迭代过程的收敛性和收敛条件。文章根据航天器热控设计的工程实际，提出一种可行的近似方法，实现了热网络方程的线性化；在此基础上对迭代法求解过程中的收敛性进行分析，确定了收敛条件下对节点热参数和时间步长的约束关系；并进一步分析时间步长与计算效率的关系，提出了以计算效率为优化目标的最优时间步长确定方法。最后通过某典型航天器热物理模型的计算验证了上述方法的正确性。

The convergence condition and the time step optimization in solving spacecraft thermal network equations by iterative method

The thermal analysis is an important part in the spacecraft thermal design and for the in-flight temperature prediction. The usual way is through solving the energy balance equations, also called the thermal network equations, of an orbiting spacecraft. And the iterative method is usually used in view of the typical nonlinear nature of the equations. However, at present, there is no theoretical criterion to judge the convergence of the iteration process. Based on the engineering practice of the spacecraft thermal design, an approximate linearization method is proposed in this paper. Then, the convergence condition is analyzed, to obtain the mutually-constrained relationship between the time step and the thermal parameter of the subject node and the time step for the calculation. Furthermore, the influence of the time step on the calculation efficiency is studied, and the optimized time step is obtained. Lastly, calculations are carried out on an established typical spacecraft thermophysical model, to verify the proposed method and the related research conclusions.