Mandeville, Milène (2026) Towards Efficient Galerkin Projection in Lagrangian ROMs for Sloshing. Master's Internship Report, Applied Mathematics.
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Abstract
This work investigates projection-based Reduced Order Models (ROMs) for Lagrangian SPH sloshing flows. We introduce a global algebraic reformulation of the SPH equations, re- placing standard neighbour loops with dense matrix-vector operations to enable both rigorous operator projection and efficient GPU-based integration for moderate particle counts. Using Proper Orthogonal Decomposition (POD) and Galerkin projection, we aim to recover a canonical Linear Time-Invariant (LTI) system. However, our analysis demonstrates that the nonlinear kernel transformations inherent to particle interactions introduce a factorized dynamics structure, where the linear system is explicitly modulated by state-dependent terms. To this end, we evaluate three strategies to approximate this nonlinearity highlighting the limitations of linearisation and Random Fourier Features for compact support kernels. Consequently, we propose an SVD-based interpolation framework as the designated strategy for future work.
| Item Type: | Thesis (Master's Internship Report) |
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| Supervisor name: | Koellermeier, J. and Luppes, R. |
| Degree programme: | Applied Mathematics |
| Thesis type: | Master's Internship Report |
| Language: | English |
| Date Deposited: | 20 Feb 2026 12:11 |
| Last Modified: | 20 Feb 2026 12:11 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/37239 |
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