On Efficient Algorithms for Filtration Related Multiscale Problems

  • This thesis deals with the numerical study of multiscale problems arising in the modelling of processes of the flow of fluid in plain and porous media. Many of these processes, governed by partial differential equations, are relevant in engineering, industry, and environmental studies. The overall task of modelling and simulating the filtration-related multiscale processes becomes interdisciplinary as it employs physics, mathematics and computer programming to reach its aim. Keeping the challenges in mind, the main focus is to overcome the limitations of accuracy, speed and memory and to develop novel efficient numerical algorithms which could, in part or whole, be utilized by those working in the field of porous media. This work has essentially four parts. A single grid basic algorithm and a corresponding parallel algorithm to solve the macroscopic Navier-Stokes-Brinkmann model is discussed. An upscaling subgrid algorithm is derived and numerically tested for the same model. Moving a step further in the line of multiscale methods, an iterative Mutliscale Finite Volume (iMSFV) method is developed for the Stokes-Darcy system. Additionally, the last part of the thesis deals with ways to incorporate changes occurring at different (meso) scale level. The flow equations are coupled with the Convection-Diffusion-Reaction (CDR) equation, which models the transport and capturing of particle concentrations. By employing the numerical method for the coupled flow and transport problem, we understand the interplay between the flow velocity and filtration.
  • Über Effiziente Algorithmen zur Lösung von Multiskalenproblemen für Filtrationsprozesse

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Verfasserangaben:Zahra Lakdawala
URN (Permalink):urn:nbn:de:hbz:386-kluedo-25291
Betreuer:Oleg Iliev
Sprache der Veröffentlichung:Englisch
Jahr der Fertigstellung:2010
Jahr der Veröffentlichung:2010
Veröffentlichende Institution:Technische Universität Kaiserslautern
Titel verleihende Institution:Technische Universität Kaiserslautern
Datum der Annahme der Abschlussarbeit:26.02.2010
Datum der Publikation (Server):26.07.2010
Freies Schlagwort / Tag:Hochskalieren
Filtration; Multiscale modelling; Numerical Flow Simulation; Numerical methods; Parallel Algorithms; Upscaling
GND-Schlagwort:Filtration; Mehrskalenmodell; Numerische Strömungssimulation; Numerisches Verfahren; Paralleler Algorithmus
Fachbereiche / Organisatorische Einheiten:Fachbereich Mathematik
DDC-Sachgruppen:5 Naturwissenschaften und Mathematik / 510 Mathematik
Lizenz (Deutsch):Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011