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http://dx.doi.org/10.18419/opus-11811
Autor(en): | Ostrowski, Lukas |
Titel: | Compressible multi-component and multi-phase flows: interfaces and asymptotic regimes |
Erscheinungsdatum: | 2021 |
Dokumentart: | Dissertation |
Seiten: | xii, 203 |
URI: | http://nbn-resolving.de/urn:nbn:de:bsz:93-opus-ds-118283 http://elib.uni-stuttgart.de/handle/11682/11828 http://dx.doi.org/10.18419/opus-11811 |
Zusammenfassung: | This thesis consists of three parts. In the first part we consider multi-component flows through porous media. We introduce a hyperbolic system of partial differential equations which describes such flows, prove the existence of solutions, the convergence in a long-time-large-friction regime to a parabolic limit system, and finally present a new numerical scheme to efficiently simulate flows in this regime. In the second part we study two-phase flows where both phases are considered compressible. We introduce a Navier-Stokes-Allen-Cahn phase-field model and derive an energy-consistent discontinuous Galerkin scheme for this system. This scheme is used for the simulation of two complex examples, namely drop-wall interactions and multi-scale simulations of coupled porous-medium/free-flow scenarios including drop formation at the interface between the two domains. In the third part we investigate two-phase flows where one phase is considered incompressible, while the other phase is assumed to be compressible. We introduce an incompressible-compressible Navier-Stokes-Cahn-Hilliard model to describe such flows. Further, we present some analytical results for this system, namely a computable expression for the effective surface tension in the system and a formal proof of the convergence to a (quasi-)incompressible system in the low Mach regime. As a first step towards a discontinuous Galerkin discretization of the system, which is based on Godunov fluxes, we introduce the concept of an artificial equation of state modification, which is examined for a basic single-phase incompressible setting. |
Enthalten in den Sammlungen: | 08 Fakultät Mathematik und Physik |
Dateien zu dieser Ressource:
Datei | Beschreibung | Größe | Format | |
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dissertation_ostrowski.pdf | 12,14 MB | Adobe PDF | Öffnen/Anzeigen |
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