Integrating Machine-Learning Photogrammetry with Nitsche-Based Parallel Finite Element Flow Simulation
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Numerical simulations of moving boundary problems, including those arising in fluid–structure interactions, require numerical methods that can robustly handle complex boundary geometries. Interface-capturing approaches meet this demand by allowing arbitrary boundary surfaces to be represented on fixed structured computational meshes. For acquiring boundary geometries associated with complex physical phenomena, photogrammetry is well suited. The integration of photogrammetry-based geometry reconstruction with interface-capturing methods could enable automated simulations without explicit meshing. In this study, we develop a fluid analysis system that automates the workflow from analysis model generation to numerical simulation by incorporating photogrammetry into an interface-capturing finite element framework. Surface geometry is reconstructed using neural implicit fields obtained via NeuS, which learns signed distance functions from multi-view images. By distributing the reconstructed neural implicit fields over fixed computational meshes, boundary surfaces are represented smoothly as analytical models. The imposition of boundary conditions on mesh-unfitted interfaces represented by implicit fields remains a key issue. To address this issue, an immersed boundary approach is employed. In particular, Nitsche’s method enables boundary conditions to be weakly enforced in a variationally consistent manner. Our method applies an approximate-delta-function-based volume-force conversion to the surface force terms arising in this method. Furthermore, we introduce a domain-decomposition-based parallel computation to accelerate the simulations. This study applies Nitsche’s method based on implicit fields to fluid analysis, and presents a quantitative accuracy assessment as well as a demonstration integrated with photogrammetry.
