In order to analyze incompressible and laminar fluid flows in presence of geometric uncertainties on the boundaries, the Non-Intrusive Polynomial Chaos method is employed, which allows the use of a deterministic fluid dynamic solver. The quantification of the fluid flow uncertainties is based on a set of deterministic response evaluations, which are obtained through a Radial Basis Function-generated Finite Differences meshless method. The use of such deterministic solver represents the key point of the analysis, thanks to the computational efficiency and similar accuracy over the traditional mesh-based numerical methods. The validation of the proposed approach is carried out through the solution of the flow past a 2D spinning cylinder near a moving wall and the flow over a backward-facing step, in presence of stochastic geometries. The applicability to practical problems is demonstrated through the investigation of geometric uncertainty effects on the forced convection of $A{l}_2{O}_3$-water nanofluid laminar flow in a grooved microchannel.

为了在边界上存在几何不确定性的情况下分析不可压缩和层状流体流动，采用了非侵入式多项式混沌方法，该方法允许使用确定性流体动力学求解器。流体流量不确定性的量化基于一组确定性响应评估，这些评估是通过径向基函数生成的有限差分无网格方法获得的。这种确定性求解器的使用代表了分析的重点，这要归功于其计算效率和与传统基于网格的数值方法相似的准确性。所提出方法的验证是通过解决流过2 D的问题来进行的在存在随机几何形状的情况下，旋转的圆柱体靠近移动的壁，并且流向后经过一个台阶。通过研究几何不确定性对强迫对流的影响，证明了对实际问题的适用性。$\mathrm{一种}{升}_2{Ø}_3$沟槽微通道中的水纳米流体层流。