Similar to the notion of h-adaptivity, where the discretization resolution is adaptively changed, I propose the notion of model adaptivity, where the underlying model (the governing equations) is adaptively changed in space and time. Specifically, this work introduces a hybrid and adaptive coupling of a 3D bulk fluid flow model with a 2D thin film flow model. As a result, this work extends the applicability of existing thin film flow models to complex scenarios where, for example, bulk flow develops into thin films after striking a surface. At each location in space and time, the proposed framework automatically decides whether a 3D model or a 2D model must be applied. Using a meshless approach for both 3D and 2D models, at each particle, the decision to apply a 2D or 3D model is based on the user-prescribed resolution and a local principal component analysis. When a particle needs to be changed from a 3D model to 2D, or vice versa, the discretization is changed, and all relevant data mapping is done on-the-fly. Appropriate two-way coupling conditions and mass conservation considerations between the 3D and 2D models are also developed. Numerical results show that this model adaptive framework shows higher flexibility and compares well against finely resolved 3D simulations. In an actual application scenario, a 3 factor speed up is obtained, while maintaining the accuracy of the solution.

翻译：类似于h-自适应（即离散化分辨率自适应变化）的概念，本文提出了模型自适应的概念，即基础模型（控制方程）在空间和时间上自适应地改变。具体而言，本研究引入了一种三维体流体流动模型与二维薄膜流动模型的混合自适应耦合方法。因此，本研究将现有薄膜流动模型的适用范围扩展到了复杂场景，例如体流体冲击表面后发展为薄膜流动的情形。在所提出的框架中，每个空间位置和时刻都会自动决定应采用三维模型还是二维模型。通过对三维和二维模型均采用无网格方法，针对每个粒子，基于用户预设的分辨率和局部主成分分析来决定应用二维或三维模型。当粒子需要从三维模型转换为二维模型（或反之）时，离散化方式将相应改变，所有相关的数据映射均实时完成。本文还建立了三维与二维模型之间适当的双向耦合条件及质量守恒考量。数值结果表明，该模型自适应框架展现出更高的灵活性，并与高分辨率三维模拟结果吻合良好。在实际应用场景中，在保持求解精度的同时实现了三倍的速度提升。