Manuel J. Castro

Elena Gaburro, Manuel J. Castro, Michael Dumbser

In this paper we propose an efficient second order well balanced finite volume method for modeling complex free surface flows at the aid of a simple diffuse interface method. The employed physical model is a two-phase model derived from the Baer-Nunziato system for compressible multi-phase flows. In particular, as proposed for the first time in Dumbser (2011), the number of equations is reduced from seven to three by assuming that the relative pressure of the gas with respect to the atmospheric reference pressure is zero, and that the gas momentum is negligible compared to the one of the liquid. The two-phase model does not make any of the classical assumptions of shallow water type systems, hence it does not neglect vertical accelerations and the free surface is not constraint to be a single-valued function, so even complex shapes as those of breaking waves can be properly captured. The resulting PDE system is solved by a novel well balanced path-conservative finite volume method on structured Cartesian grids, which is able to preserve exactly the equilibrium states even in the presence of obstacles. It furthermore automatically computes the location of the water-air interfaces, and assures low numerical dissipation at the free surface thanks to a novel Osher-Romberg-type Riemann solver. Finally, high computational performance is guaranteed by an efficient parallel implementation on a GPU-based platform that reaches the efficiency of twenty million of volumes processed per seconds and makes it possible to employ even very fine meshes. The validation of our new well balanced scheme is carried out by comparing the obtained numerical results against existing analytical, numerical and experimental reference solutions for a large number of test cases, among which oscillating elliptical drops, dambreak problems, breaking waves, over topping weir flows, and wave impact problems.

C. Escalante, T. Morales de Luna, M. J. Castro

We consider the depth-integrated non-hydrostatic system derived by Yamazaki et al. An efficient formally second-order well-balanced hybrid finite volume finite difference numerical scheme is proposed. The scheme consists of a two-step algorithm based on a projection-correction type scheme initially introduced by Chorin-Temam [15]. First, the hyperbolic part of the system is discretized using a Polynomial Viscosity Matrix path-conservative finite volume method. Second, the dispersive terms are solved by means of compact finite differences. A new methodology is also presented to handle wave breaking over complex bathymetries. This adapts well to GPU-architectures and guidelines about its GPU implementation are introduced. The method has been applied to idealized and challenging experimental test cases, which shows the efficiency and accuracy of the method.

Mehmet Batuhan Duman, Alejandro Carnero, Cristian Martín et al.

Foam formation in Wastewater Treatment Plants (WTPs) is a major challenge that can reduce treatment efficiency and increase costs. The ability to automatically examine changes in real-time with respect to the percentage of foam can be of great benefit to the plant. However, large amounts of labeled data are required to train standard Machine Learning (ML) models. The development of these systems is slow due to the scarcity and heterogeneity of labeled data. Additionally, the development is often hindered by the fact that different WTPs do not share their data due to privacy concerns. This paper proposes a new framework to address these challenges by combining Federated Learning (FL) with the state-of-the-art base model for image segmentation, Segment Anything Model 2 (SAM2). The FL paradigm enables collaborative model training across multiple WTPs without centralizing sensitive operational data, thereby ensuring privacy. The framework accelerates training convergence and improves segmentation performance even with limited local datasets by leveraging SAM2's strong pre-trained weights for initialization. The methodology involves fine-tuning SAM2 on distributed clients (edge nodes) using the Flower framework, where a central Fog server orchestrates the process by aggregating model weights without accessing private data. The model was trained and validated using various data collections, including real-world images captured at a WTPs in Granada, Spain, a synthetically generated foam dataset, and images from publicly available datasets to improve generalization. This research offers a practical, scalable, and privacy-aware solution for automatic foam tracking in WTPs. The findings highlight the significant potential of integrating large-scale foundational models into FL systems to solve real-world industrial challenges characterized by distributed and sensitive data.