Objective  The computational simulation of external heat flux in space is a crucial aspect of spacecraft thermal management design and ground test validation. Monte Carlo (MC) techniques are currently the prevailing approach for addressing spacecraft external heat flux calculations. Nevertheless, the inherent shortcoming of MC methods is their comparatively slow rate of convergence. To achieve a statistical solution for the external heat flux approximating the precise solution, a considerable number of rays must be emitted, resulting in substantial computational overhead. Consequently, the exploration of efficient algorithms for solving external heat flux is of paramount importance. To this end, a comprehensive examination of Earth radiative external heat flux is conducted, leading to the development of an innovative computational algorithm. The findings of this study will offer valuable theoretical insights for enhancing the calculation efficiency of Earth infrared and albedo radiation external heat flux, and serve as a reference for research on the localization of spacecraft external heat flux computation software.

  Methods  Firstly, an analysis and comparison of the contribution of each random variable dimension within the Earth radiative external heat flux integral are conducted, revealing that the foremost four dimensions of random variables yield the most significant contributions to the integral. Subsequently, Quasi-Monte Carlo (QMC) techniques are employed in lieu of traditional MC methods for the first four dimensions of the external heat flux integral to sample the ray emission point and direction for the target surface element in question, while MC is utilized for the remaining integration dimensions. This novel algorithm combines both MC and QMC approaches to compute the external heat flux. Lastly, a spacecraft serves as a computational example to ascertain the accuracy and convergence rate of the external heat flux through a large-scale ray tracing experiment.

  Results and Discussions   The comparative accuracy of the three methods employed to calculate Earth infrared and albedo external heat flux reveals the superior performance of hybrid-QMC, followed by Latin Hypercube Sampling (LHS), and lastly, the least accurate being MC (Fig.7-8). When utilizing the hybrid-QMC approach to solve Earth albedo and infrared radiative external heat flux, the convergence rate surpasses that of the other two methods. In ray tracing individual surface elements to solve the Earth radiative external heat flow, the surface elements without reflected rays can obtain a better convergence speed. For these surface elements, the hybrid-QMC method has the most significant improvement in the convergence speed of the external heat flow accuracy (Tab.6-9).

  Conclusions  The importance of each integration variable dimension in the Earth radiative external heat flow is analyzed, and the results show that the first four integration dimensions contribute the most to the integration of the Earth albedo and infrared radiative external heat flow. A spacecraft is used as an example for calculation, and the results show that the hybrid-QMC method has the highest accuracy and convergence speed when dealing with the external heat flow of different surface elements of the spacecraft. The advantage of hybrid-QMC is more prominent when there is no reflection behavior of the ray emitted by the surface element. This method can provide some reference to improve the speed and accuracy of the spacecraft external heat flow calculation.