Designing spray nozzles requires predicting how geometry shapes transient two-phase breakup, but high-fidelity volume-of-fluid (VOF) simulations with adaptive mesh refinement (AMR) are too expensive for iterative design exploration. Standard surrogate models are also challenged by this setting because both the liquid--gas interface and the underlying adaptive discretization evolve across time and geometries. We introduce a geometry-conditioned latent surrogate trained on 797 two-phase nozzle simulations that addresses this by encoding the AMR cell-density field, rather than the full multi-channel flow state, as a compact proxy for where the solver concentrates resolution. From this representation, the model reconstructs transient density evolution and nozzle geometry, and a lightweight second stage recovers the remaining flow variables. On held-out simulations, the method accurately captures key interface dynamics while reducing inference time to 0.045 seconds per trajectory, corresponding to a speed-up of more than $6\times10^4$ relative to Basilisk CFD. These results suggest that AMR refinement structure can serve as a compact and learnable representation for geometry-conditioned surrogate modeling of transient two-phase flows.

翻译：设计喷雾喷嘴需要预测几何形状如何影响瞬态两相破碎过程，但采用自适应网格细化（AMR）的高保真流体体积（VOF）模拟对于迭代设计探索而言成本过高。标准代理模型在此场景下同样面临挑战，因为液-气界面及底层自适应离散化均随时间与几何形状演变。我们提出一种几何条件化潜空间代理模型，该模型基于797个两相喷嘴模拟数据进行训练，通过编码AMR单元密度场（而非完整多通道流动状态）作为求解器集中分辨率的紧凑代理。基于该表示，模型能够重建瞬态密度演化与喷嘴几何形状，并通过轻量级第二阶段恢复其余流动变量。在保留模拟数据集上，该方法准确捕捉关键界面动力学，同时将推理时间降至每轨迹0.045秒，相比Basilisk CFD实现超过6×10⁴倍的加速。这些结果表明，AMR细化结构可作为瞬态两相流几何条件化代理建模的紧凑且可学习表示。