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Mode decomposition methods, such as proper orthogonal decomposition and dynamic mode decomposition (DMD), have introduced a novel data-driven approach for flow prediction. These methods aim to identify a collection of modes that capture the essential flow features. Subsequently, the flow field data are projected onto these modes to reconstruct and predict the evolution of the flow field. However, due to their inherent linearity, mode decomposition methods are limited in effectively handling unsteady and nonlinear flow exhibiting significant nonlinearities. In this study, we propose a spectral graph convolutional deep neural network (SGC-DNN). It employs the eigenvectors of the Laplacian matrix as modes to fully utilize the adjacency information within the graph structure to solve flow on an unstructured grid better. Additionally, we employ a DNN (deep neural network) to model the temporal evolution of each mode, thereby enhancing the model's adaptability to nonlinear flow fields. To evaluate the performance of our proposed SGC-DNN, we compare its prediction results with those obtained using DMD and DNN for the flow around a cylinder on unstructured grids at various Reynolds numbers (ranging from 1000 to 500 000). We also compared the predictive results of these three models for flow with complex geometries, such as the Da Vinci pipeline flow and intracranial aneurysm blood flow. The comparative analysis demonstrates that SGC-DNN outperformed the other models, yielding lower L2 relative errors and higher R2 values. These outcomes highlight the superiority of SGC-DNN in accurately predicting unsteady and nonlinear flow characterized by graph structures.
Mode decomposition methods, such as proper orthogonal decomposition and dynamic mode decomposition (DMD), have introduced a novel data-driven approach for flow prediction. These methods aim to identify a collection of modes that capture the essential flow features. Subsequently, the flow field data are projected onto these modes to reconstruct and predict the evolution of the flow field. However, due to their inherent linearity, mode decomposition methods are limited in effectively handling unsteady and nonlinear flow exhibiting significant nonlinearities. In this study, we propose a spectral graph convolutional deep neural network (SGC-DNN). It employs the eigenvectors of the Laplacian matrix as modes to fully utilize the adjacency information within the graph structure to solve flow on an unstructured grid better. Additionally, we employ a DNN (deep neural network) to model the temporal evolution of each mode, thereby enhancing the model's adaptability to nonlinear flow fields. To evaluate the performance of our proposed SGC-DNN, we compare its prediction results with those obtained using DMD and DNN for the flow around a cylinder on unstructured grids at various Reynolds numbers (ranging from 1000 to 500 000). We also compared the predictive results of these three models for flow with complex geometries, such as the Da Vinci pipeline flow and intracranial aneurysm blood flow. The comparative analysis demonstrates that SGC-DNN outperformed the other models, yielding lower L2 relative errors and higher R2 values. These outcomes highlight the superiority of SGC-DNN in accurately predicting unsteady and nonlinear flow characterized by graph structures.
In this study, the particle-laden flow in the wake of a static and a rotating cylinder at Reynolds number of 140 000 was investigated using the Reynolds Averaged Navier–Stokes numerical approach. Three turbulence models such as k–ω shear stress transport, Reynolds stress model, and local-correlation transition model (LCTM) were selected to predict the flow topology. Lagrangian approach with one-way coupling was used to track solid spherical particles of different sizes (0.01, 0.1, 2.5, 10, and 50 μm). The study reveals that LCTM is the most accurate to predict the flow topology in both cases. Cylinder's rotation generates different effects on flow structure. It breaks the wake's symmetry and reduces its width, and increases the frequency of vortex shedding and the size of the recirculation zone. Particle transport analysis has revealed that particles' response to the flow depends on their Stokes number and wake flow topology. Particles of 0.01, 0.1, and 2.5 μm distribute in and around vortex cores, while particles of 10 and 50 μm do not penetrate vortex cores. Instead, 10 μm particles accumulate mainly around the periphery of vortices, while 50 μm particles skip the vortex street to the thin shear flow region between vortices to be transported by the mainstream flow. Finally, cylinder rotation reduces the particle spread in the vertical direction and shifts all particle distributions in the cylinder's rotation direction. Analysis of particle dispersion functions showed that cylinder's rotation reduces differences in dispersion extent depending on particle size.
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