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Efficient modeling and simulation of uncertainties in computational fluid dynamics (CFD) remains a crucial challenge. In this paper, we present the first stochastic Galerkin (SG) lattice Boltzmann method (LBM) built upon the generalized polynomial chaos (gPC). The proposed method offers an efficient and accurate approach that depicts the propagation of uncertainties in stochastic incompressible flows. Formal analysis shows that the SG LBM preserves the correct Chapman–Enskog asymptotics and recovers the corresponding macroscopic fluid equations. Numerical experiments, including the Taylor–Green vortex flow, lid-driven cavity flow, and isentropic vortex convection, are presented to validate the solution algorithm. The results demonstrate that the SG LBM achieves the expected spectral convergence and the computational cost is significantly reduced compared to the sampling-based non-intrusive approaches, e.g., the routinely used Monte Carlo method. We obtain a speedup factor of 5.72 compared to Monte Carlo sampling in a randomized two-dimensional Taylor–Green vortex flow test case. By leveraging the accuracy and flexibility of LBM and the efficiency of gPC-based SG, the proposed SG LBM provides a powerful framework for uncertainty quantification in CFD practice. • First stochastic Galerkin lattice Boltzmann method. • Efficient conversion between polynomial chaos and collocation point- wise values. • Spectral convergence verified in numerical experiments. • Formal Chapman–Enskog consistency to recover macroscopic transport equations. • Speedup factor of 5.72 compared to Monte Carlo sampling for 2D Taylor–Green vortex. [ABSTRACT FROM AUTHOR]

[Display omitted] Despite the flourishing studies of droplet interfacial boiling, the boiling upon vibratory surfaces, which may cause vigorous liquid–vapor-solid interactions, has rarely been investigated. Enhanced boiling normally can be gained from rapid removal of vapor and disturbance of liquid–vapor interface. We hypothesize that the vibratory surfaces enhance both effects with new intriguing phenomena and thus, attain an enhanced boiling heat transfer. We experimentally investigated the impacting fluid dynamics and coupled heat transfer patterns of multiple droplets and a single droplet impinging on still and vibratory surfaces of various materials and different wettability. The boiling under vibratory surfaces with increased vibration velocity amplitude and enhanced wettability can be enhanced by 80% in heat transfer coefficient and Nusselt number, which is attributed to several reasons: shortened bubble lifespan, thinner and smaller bubbles, and enhanced disturbances in liquid–vapor interfaces. The vibration also delays the Leidenfrost point when the droplet impacts a descending surface, which shows that the droplet impact moment (vibration phase angle) is particularly crucial. The descending surface releases the generated vapor actively and facilitates liquid–solid contact, thereby delaying the Leidenfrost. From fundamentals to application, this article strengthens our understanding of vibrated interfacial boiling in scenarios closer to multiple natural processes and practical industries. [ABSTRACT FROM AUTHOR]