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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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Author:Zahra Lakdawala
URN (permanent link):urn:nbn:de:hbz:386-kluedo-25291
Advisor:Oleg Iliev
Document Type:Doctoral Thesis
Language of publication:English
Year of Completion:2010
Year of Publication:2010
Publishing Institute:Technische Universität Kaiserslautern
Granting Institute:Technische Universität Kaiserslautern
Acceptance Date of the Thesis:2010/02/26
Date of the Publication (Server):2010/07/26
Filtration; Multiscale modelling; Numerical Flow Simulation; Numerical methods; Parallel Algorithms; Upscaling
GND-Keyword:Filtration; Mehrskalenmodell; Numerische Strömungssimulation; Numerisches Verfahren; Paralleler Algorithmus
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:5 Naturwissenschaften und Mathematik / 510 Mathematik
Licence (German):Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011