Uniform error estimates of a bi-fidelity method for a kinetic-fluid coupled model with random initial inputs in the fine particle regime are proved in this paper. Such a model is a system coupling the incompressible Navier-Stokes equations to the Vlasov-Fokker-Planck equations for a mixture of the flows with distinct particle sizes. The main analytic tool is the hypocoercivity analysis for the multi-phase Navier-Stokes-Vlasov-Fokker-Planck system with uncertainties, considering solutions in a perturbative setting near the global equilibrium. This allows us to obtain the error estimates in both kinetic and hydrodynamic regimes.

翻译：本文证明了在细颗粒状态下，一种针对具有随机初始输入的动理学-流体耦合模型的双保真度方法的均匀误差估计。该模型是耦合不可压缩Navier-Stokes方程与Vlasov-Fokker-Planck方程的系统，用于描述具有不同颗粒尺寸的流动混合物。主要分析工具是对含不确定性的多相Navier-Stokes-Vlasov-Fokker-Planck系统进行弱耗散性分析，考虑在全局平衡态附近摄动设定下的解。这使得我们能够在动理学区域和流体力学区域均获得误差估计。