Pressure robust methods for incompressible flow
| Thesis title in Czech: | Tlakově robustní metody v nestlačitelném proudění |
|---|---|
| Thesis title in English: | Pressure robust methods for incompressible flow |
| Key words: | nestlačitelné proudění|Navier–Stokesovy a Stokesovy rovnice|tlakově robustní metody|divergence-free metody|smíšené konečné prvky |
| English key words: | incompressible flow|Navier–Stokes and Stokes equations|pressure-robust methods|divergence-free methods|mixed finite elements |
| Academic year of topic announcement: | 2023/2024 |
| Thesis type: | Bachelor's thesis |
| Thesis language: | angličtina |
| Department: | Mathematical Institute of Charles University (32-MUUK) |
| Supervisor: | Mgr. Jan Blechta, Ph.D. |
| Author: | Nail Sultanbekov - assigned and confirmed by the Study Dept. |
| Date of registration: | 20.03.2024 |
| Date of assignment: | 20.03.2024 |
| Confirmed by Study dept. on: | 20.03.2024 |
| Date and time of defence: | 11.09.2025 08:30 |
| Date of electronic submission: | 17.07.2025 |
| Date of submission of printed version: | 17.07.2025 |
| Opponents: | Pablo Alexei Gazca Orozco, Ph.D. |
| Guidelines |
| Cílem bakalářské práce je seznámit se s numerickým řešením nestlačitelného proudění s důrazem na tlakově robustní metody. Studující nastuduje přehledovou literaturu k tématu, zejména [John, Linke, Merdon, Neilan, Rebholz 2017]. Součástí práce je implementace a numerické experimenty za pomocí softwarové knihovny Firedrake nebo podobné. |
| References |
| John, V., Linke, A., Merdon, C., Neilan, M., Rebholz, L.G. On the divergence constraint in mixed finite element methods for incompressible flows, SIAM Rev. 59(3), 492–544 (2017), DOI 10.1137/15M1047696
Neilan, M. The Stokes Complex: A review of exactly divergence-free finite element pairs for incompressible flows, 75 Years of Mathematics of Computation, 141–158, Contemp. Math. 754, AMS 2020 Arnold, D.N. Finite element exterior calculus, CBMS-NSF Regional Conf. Ser. in Appl. Math., 93 Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2018. xi+120 pp, DOI 10.1137/1.9781611975543 Scott, L.R., Vogelius, M. Conforming finite element methods for incompressible and nearly incompressible continua, Technical Note BN-1018, 1984, URL https://apps.dtic.mil/sti/pdfs/ADA141117.pdf Scott, L.R., Vogelius, M. Norm estimates for a maximal right inverse of the divergence operator in spaces of piecewise polynomials, RAIRO Modél. Math. Anal. Numér.19(1985), no.1, 111–143, DOI 10.1051/m2an/1985190101111 Boffi, D., Brezzi, F., Fortin, M. Mixed finite element methods and applications, Springer Series in Computational Mathematics 44, Springer, Heidelberg 2013, DOI 10.1007/978-3-642-36519-5 |