To address the computational challenges posed by nonlinear collision kernels in the Smoluchowski equation, this study proposes a universal preprocessing algorithm for the average kernel method based on the Gauss-Laguerre quadrature for double integrals. With this algorithm, the numerical code accurately and efficiently determines the pre-exponential factor of the average kernel. Additionally, the exact pre-exponential factors of the four fundamental average kernels and their associated truncation error estimations were analyzed. The results demonstrate the reasonability and reliability of the preprocessing algorithm.

翻译：针对Smoluchowski方程中非线性碰撞核带来的计算挑战，本研究提出了一种基于高斯-拉盖尔求积的双重积分平均核方法通用预处理算法。该算法使数值代码能够精确高效地确定平均核的指前因子。此外，本文分析了四种基本平均核的精确指前因子及其对应的截断误差估计。结果表明该预处理算法具有合理性与可靠性。