E-Thesis 262 views
Numerically-informed neural networks for degree adaptive unsteady incompressible flow simulations / VALERIA RAMUDO
Swansea University Author: VALERIA RAMUDO
DOI (Published version): 10.23889/SUthesis.69401
Abstract
The need for transient incompressible flow simulations in science and engineering has driven the demand for high-order methods over conventional low-order finite element and finite volume approaches. High-order methods offer greater accuracy and efficiency in capturing the complex, time-dependent be...
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Swansea, Wales, UK
2025
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| Institution: | Swansea University |
| Degree level: | Doctoral |
| Degree name: | Ph.D |
| Supervisor: | Sevilla, Ruben ; Hassan, Oubay |
| URI: | https://cronfa.swan.ac.uk/Record/cronfa69401 |
| Abstract: |
The need for transient incompressible flow simulations in science and engineering has driven the demand for high-order methods over conventional low-order finite element and finite volume approaches. High-order methods offer greater accuracy and efficiency in capturing the complex, time-dependent behaviour of fluid systems because of the lower dissipation and dispersion of high-order approximations. Traditional low-order methods often require highly refined meshes to achieve comparable accuracy, leading to higher computational costs.This thesis focuses on problems where flow features such as vortices or gust pertur-bations need to be propagated over long distances. These flow features can be more accurately propagated using high-order methods, but their localised nature suggests that incorporating degree adaptive schemes can lead to significantly more efficient sim-ulations by only employing high-order approximations where needed. Discontinuous Galerkin methods have gained significant popularity and provide an easy-to-implement framework for degree adaptivity. In particular, the hybridisable discontinuous Galerkin is adopted in this work and implemented in Fortran 90.This thesis provides two original scientific contributions. First, a conservative projec-tion scheme has been developed and implemented to enable efficient degree adaptive simulations for transient incompressible flows. The proposed scheme is found to remove all the numerical artefacts shown by a standard adaptive process due to the violation of the free-divergence condition when projecting a solution from a space of polynomials of a given degree to a space of polynomials with a lower degree. Second, a novel degree adaptive procedure is designed by using a trained artificial neural network to predict the solution at a future time from the solution at the current time. The procedure is shown to perform the degree adaptivity in places where flow features will travel in the future and prevents the traditional requirement to perform degree adaptivity cycles within a time step. |
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| Keywords: |
transient incompressible flow, high-order methods, hybridisable discontinuous Galerkin, degree adaptivity, artificial neural network |
| College: |
Faculty of Science and Engineering |
| Funders: |
EPSRC DTA; IHPC Singapore |