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Dettaglio Insegnamento
| Academic Year |
2021/2022 |
| Name |
Dott. - MI (1385) Modelli e Metodi Matematici per l'Ingegneria / Mathematical Models and Methods in Engineering |
| Programme Year |
1 |
| ID Code |
057412 |
| Course Title |
NUMERICAL METHODS FOR THE GEOSCIENCES |
| Course Type |
MONODISCIPLINARE |
| Credits (CFU / ECTS) |
5.0 |
| Course Description |
We will address the following topics, progressing in parallel with mathematical and numerical modeling:
- Single phase flow in porous media: introduction, definitions and governing equations. Discretization methods: the advantages of mixed methods vs primal methods, with a focus on heterogeneities in material properties. Exercise session: simple numerical simulations with the software Porepy.
- Discretization of complex domains (layered, heterogeneous media and presence of thin inclusions such as fractures). Coupled hybrid dimensional PDEs. Flexible numerical methods for non-standard grids (such as VEM). Exercise session: numerical experiments with Porepy.
- Transport phenomena in porous media (passive transport, two-phase flow). Implicit and explicit discretization schemes, time step restrictions, choice of the numerical flux and its effects.
- Poroelasticity: a primer on linear elasticity, introduction to Biot's theory, coupled mathematical model. Invited seminar on solution strategies (monolithic vs iterative splittings) by J.Both (University of Bergen). Exercise session: numerical tests in Porepy.
- Reactive transport: mathematical modeling by advection-diffusion-reaction PDEs.
Solution strategies: fully coupled vs iterative and non-iterative splittings; choice of the time advancing scheme; stiffness due to the coexistence of time scales. Exercise session: comparison of the strategies on a simple one-dimensional problem. |
| Scientific-Disciplinary Sector (SSD)
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Alphabetical group
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Professor
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Course details
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From (included)
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To (excluded)
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A
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ZZZZ
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Scotti Anna, Fumagalli Alessio
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