Adaptive coupling of 3D and 2D fluid flow models

TL;DR

The paper tackles the challenge of simulating flows that involve both bulk 3D regions and thin-film 2D regions by introducing a fully meshfree, model-adaptive coupling between a 3D Navier–Stokes solver and a pseudo-2D discrete droplet thin-film model. It develops PCA- and resolution-based per-particle criteria to auto-detect where a thin-film model should apply, and provides detailed discretization-switching procedures along with mass-conserving data transfer and a dynamic buffer (ghost) region for two-way coupling. Key contributions include the automatic, localized model transitions, conservative data mapping, and ghost-based data communication that enable near-full 3D accuracy with substantial speedups in representative test cases such as cleaning jets and automotive water crossing. The approach offers practical impact for complex fluid-structure interactions and free-surface problems where film formation and bulk flows compete, with potential extensions to curved or moving surfaces and broader model pairs.

Abstract

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.

Figures (17)

• Figure 1: Schematic of model adaptivity between a 3D bulk flow model (blue) and 2D thin film flow model (maroon). The surface over which the fluid is flowing is shown in black. The thin film flow model is shown to be of a smaller height since it relies on a surface discretization only, while the entire bulk is discretized for the bulk flow model. Throughout this work, the bulk flow model is three-dimensional, while the thin film model is two-dimensional. Lower dimensional representations are used in this figure for ease of visualization.
• Figure 2: Resolution based criterion for detecting bulk to thin film transition. Wall particles are marked in green, interior particles in blue, and free surface particles in orange. The wall particle at which the bulk to thin film transition criterion is being evaluated is marked with an additional black circle, with its neighbourhood highlighted. The wall is marked in grey. Note that throughout this work a 3D bulk model and 2D thin film model is considered. This figure shows a lower dimensional schematic for the ease of visualization.
• Figure 3: PCA eigenvalue and eigenvector criteria for detecting bulk to thin film transition. Wall particles are marked in green, interior particles in blue, and free surface particles in orange. The wall particle at which the bulk to thin film transition criterion is being evaluated is marked with an additional black circle, with its neighbourhood highlighted, and normal $\vec{n}$ marked. The wall is marked in grey, and eigenvectors of the local variance matrix are marked as $\vec{w}_k$. Note that throughout this work a 3D bulk model and 2D thin film model is considered. This figure shows a lower dimensional schematic for the ease of visualization.
• Figure 4: Performing model transition from the bulk model to the thin film model (figure a), and from the thin film model to the bulk model (figure b). Bulk particles are shown in blue, and thin film particles in maroon. Note that throughout this work a 3D bulk model and 2D thin film model is considered. This figure shows a lower dimensional schematic for the ease of visualization.
• Figure 5: Creation of ghost particles. Bulk particles are shown in blue, and thin film particles in maroon. Ghost particles are shown in a brighter shade for each model. Note that throughout this work a 3D bulk model and 2D thin film model is considered. This figure shows a lower dimensional schematic for the ease of visualization. A representation of the same in $\mathbb{R}^3$ is shown in the results section in Figure \ref{['Fig:AdvectionDomain']}.

Theorems & Definitions (9)

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