In this paper, three efficient ensemble algorithms are proposed for fast-solving the random fluid-fluid interaction model. Such a model can be simplified as coupling two heat equations with random diffusion coefficients and a friction parameter due to its complexity and uncertainty. We utilize the Monte Carlo method for the coupled model with random inputs to derive some deterministic fluid-fluid numerical models and use the ensemble idea to realize the fast computation of multiple problems. Our remarkable feature of these algorithms is employing the same coefficient matrix for multiple linear systems, significantly reducing the computational cost. By data-passing partitioned techniques, we can decouple the numerical models into two smaller sub-domain problems and achieve parallel computation. Theoretically, we derive that both algorithms are unconditionally stable and convergent. Finally, numerical experiments are conducted not only to support the theoretical results but also to validate the exclusive feature of the proposed algorithms.
翻译:本文提出了三种高效的混合算法, 用于快速解决随机流体流体互动模型。 这样的模型可以简化, 因为它复杂和不确定, 将两个热方程式与随机扩散系数和摩擦参数相混合。 我们使用蒙特卡洛方法来混合模型, 加上随机输入, 得出一些确定性流体流体流体数字模型, 并使用共和概念快速计算多种问题。 我们这些算法的显著特征是, 对多个线性系统采用相同的系数矩阵, 大幅降低计算成本。 通过数据覆盖分隔技术, 我们可以将数字模型分解为两个较小的次域问题, 并实现平行计算。 从理论上讲, 我们推论上说, 这两种算法都是无条件稳定和一致的。 最后, 数字实验不仅支持理论结果, 也验证了拟议算法的独有特征 。