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1	Computational Techniques for Efficient Solution of Discretized Biot's Theory for Fluid Flow in Deformable Porous Media Lee, Im Soo 09 September 2008 (has links) In soil and rock mechanics, coupling effects between geomechanics field and fluid-flow field are important to understand many physical phenomena. Coupling effects in fluid-saturated porous media comes from the interaction between the geomechanics field and the fluid flow. Stresses subjected on the porous material result volumetric strains and fluid diffusion in the pores. In turn, pore pressure change cause effective stresses change that leads to the deformation of the geomechanics field. Coupling effects have been neglected in traditional geotechnical engineering and petroleum engineering however, it should not be ignored or simplified to increases reliability of the results. The coupling effect in porous media was theoretically established in the poroelasticity theory developed by Biot, and it has become a powerful theory for modeling three-dimensional consolidation type of problem. The analysis of the porous media with fully-coupled simulations based on the Biot's theory requires intensive computational effort due to the large number of interacting fields. Therefore, advanced computational techniques need to be exploited to reduce computational time. In order to solve the coupled problem, several techniques are currently available such as one-way coupling, partial-coupling, and full-coupling. The fully-coupled approach is the most rigorous approach and produces the most correct results. However, it needs large computational efforts because it solves the geomechanics and the fluid-flow unknowns simultaneously and monolithically. In order to overcome this limitation, staggered solution based on the Biot's theory is proposed and implemented using a modular approach. In this thesis, Biot's equations are implemented using a Finite Element method and/or Finite Difference method with expansion of nonlinear stress-strain constitutive relation and multi-phase fluid flow. Fully-coupled effects are achieved by updating the compressibility matrix and by using an additional source term in the conventional fluid flow equation. The proposed method is tested in multi-phase FE and FD fluid flow codes coupled with a FE geomechanical code and numerical results are compared with analytical solutions and published results. / Ph. D. Biot's theory fully-coupled solution finite elements
2	Viscosity solutions of fully nonlinear parabolic systems Liu, Weian, Yang, Yin, Lu, Gang January 2002 (has links) In this paper, we discuss the viscosity solutions of the weakly coupled systems of fully nonlinear second order degenerate parabolic equations and their Cauchy-Dirichlet problem. We prove the existence, uniqueness and continuity of viscosity solution by combining Perron's method with the technique of coupled solutions. The results here generalize those in [2] and [3]. Viscosity solutions Perron's method coupled solution Mathematics
3	Desenvolvimento de modelo numerico tridimensional e eliptico para o estudo de escoamentos no interior de dutos cilindricos / Development of three-dimensional and elliptical numerical model for the study of fluid flow in cylindrical ducts Lopes, Gabriela Cantarelli 27 June 2008 (has links) Orientador: Jose Roberto Nunhez / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Quimica / Made available in DSpace on 2018-08-11T08:15:27Z (GMT). No. of bitstreams: 1 Lopes_GabrielaCantarelli_M.pdf: 1710566 bytes, checksum: efab0c6308734536b15c2ef91d4d8337 (MD5) Previous issue date: 2008 / Resumo: Processos que envolvem escoamentos de fluidos no interior de dutos estão presentes em muitas aplicações industriais. Na indústria petroquímica um desses processos que vem se tornando cada vez mais importante é o craqueamento catalítico de frações pesadas do petróleo, já que as converte em frações leves e mais nobres. Por causa da crescente demanda mundial por gasolina e GLP e à sua alta rentabilidade para uma refinaria de petróleo, unidades de craqueamento catalítico em leito fluidizado (FCC) estão presentes em todo o mundo. Testes experimentais costumam ser usados no estudo dos fenômenos envolvidos nesse processo. Porém esse tipo de análise possui alto custo, que pode ser reduzido com o uso de simulações computacionais em seu estudo inicial. Assim, o objetivo deste trabalho foi desenvolver um modelo tridimensional e elíptico, em linguagem Fortran, capaz de fornecer dados para a análise preliminar de escoamentos no interior de reatores de FCC. Na modelagem desses problemas são usadas equações diferenciais parciais, e essas não possuem solução analítica conhecida, sendo necessário o emprego de métodos numéricos para esse fim. Neste trabalho foi usado o Método dos Volumes Finitos, que tem a função de substituir as equações diferenciais parciais por equações algébricas aplicadas a pequenos volumes de controle finitos pertencentes ao domínio. Uma das maiores dificuldades encontradas no tratamento numérico de escoamentos incompressíveis é a determinação de um campo de pressão que satisfaça a Equação da Continuidade. Esse problema foi resolvido fazendo-se uso da abordagem acoplp.da de solução. Para análise do modelo foram obtidos perfis numéricos de velocidade e pressão para fluidos escoando em regimes laminar e turbulento, que foram validados usando-se os dados obtidos com a solução analítica das equações, por correlações (semi-) empíricas ou por dados experimentais, conforme cada um dos casos. Notou-se que o modelo representa muito bem casos laminares, e gue 11.oS casos turbulentos foi necessário um maior refino da malha próximo a parede do tubo. Também foram feitas simulações para que se pudessem observar as características tridimensionais, elípticas e transientes da modelagem do escoamento. De maneira geral o modelo se mostrou bastante rápido, convergindo em poucas iterações. Palavras-Chave: Fluidodinâmica computacional; dutos cilíndricos; modelo tridimensional e elíptico; método dos Volumes Finitos; solução acoplada; turbulência / Abstract: Processes involving fluid flow in tubes are present in many industrial applications. In petrochemical industry one of these processes that are becoming more and more important is the fluid catalytic cracking of heavy petroleum fractions. This fact is due to the process capacity to convert heavy fractions in light and valuable ones. Because of the increasingly worldwide demand for gasoline and LPG and its high yield for a petroleum refinery, fluid catalytic cracking (FCC) units are present in the whole world. Experimental tests are used in the study of the phenomena involved in this processo However this kind of analysis has high cost which can be reduced by using computational simulations in its initial study. Thus, the aim of this work was the development of a three-dimensional and elliptical mo dei in Fortran language in order to provide data for fluid flow preliminary analysis in FCC reactors. Partial differential equations were used in the modeling of these problems. These equations do not have known analytical solution, being necessary therefore the use of numerical methods. In this work the Finite Volume Method were applied with this purpose. This method has as a role to substitute the partial differential equations of the mo dei for algebric equations applied to small finite control volumes of the domain. One of the biggest difficulties found in the numerical treatment of incompressible fluid flows is the determination of apressure field that satisfies the Continuity Equation. This problem was solved using the coupled solution approach. For model analysis, numerical velocity and pressure proJ:iles for laminar and turbulent flows were obtained, that had been validated using the data obtained through the analytical solution of the equations, by empirical correlations or by experimental data, according to each one of the cases. The model represented well laminar cases, and in the turbulent ones the mesh had to be more refined near the tube wall. Other simulations were performed, in aQalyzing the three-dimensional, elliptical and transient model characteristics. In general, the mo dei was very fast, converging in a few interations. Keywords: Computational fluid dyn~mic; cylindrical ducts; three-dimensional and elliptical model; Finite Volume Method; coupled solution; turbulence / Mestrado / Desenvolvimento de Processos Químicos / Mestre em Engenharia Química Fluidodinâmica computacional Tubos Modelos matemáticos Turbulência Método dos volumes finitos Computational fluid dynamic Cylindrical ducts Three-dimensional model Elliptical model Coupled solution Finite volume method
4	Methodenentwicklung zur Simulation von Strömungen mit freier Oberfläche unter dem Einfluss elektromagnetischer Wechselfelder Beckstein, Pascal 16 February 2018 (has links) (PDF) Im Bereich der industriellen Metallurgie und Kristallzüchtung treten bei zahlreichen Anwendungen, wo magnetische Wechselfelder zur induktiven Beeinflussung von leitfähigen Werkstoffen eingesetzt werden, auch Strömungen mit freier Oberfläche auf. Das Anwendungsspektrum reicht dabei vom einfachen Aufschmelzen eines Metalls in einem offenen Tiegel bis hin zur vollständigen Levitation. Auch der sogenannte RGS-Prozess, ein substratbasiertes Kristallisationsverfahren zur Herstellung siliziumbasierter Dünnschichtmaterialien, ist dafür ein Beispiel. Um bei solchen Prozessen die Interaktion von Magnetfeld und Strömung zu untersuchen, ist die numerische Simulationen ein wertvolles Hilfsmittel. Für beliebige dreidimensionale Probleme werden entsprechende Berechnungen bisher durch eine externe Kopplung kommerzieller Programme realisiert, die für Magnetfeld und Strömung jeweils unterschiedliche numerische Techniken nutzen. Diese Vorgehensweise ist jedoch im Allgemeinen mit unnötigem Rechenaufwand verbunden. In dieser Arbeit wird ein neu entwickelter Methodenapparat auf Basis der FVM vorgestellt, mit welchem sich diese Art von Berechnungen effizient durchführen lassen. Mit der Implementierung dieser Methoden in foam-extend, einer erweiterten Version der quelloffenen Software OpenFOAM, ist daraus ein leistungsfähiges Werkzeug in Form einer freien Simulationsplattform entstanden, welches sich durch einen modularen Aufbau leicht erweitern lässt. Mit dieser Plattform wurden in foam-extend auch erstmalig dreidimensionale Induktionsprozesse im Frequenzraum gelöst. Metallurgie Kristallzüchtung Elektroprozesstechnik elektromagnetisches Prozessieren Optimierung Simulation RGS Ribbon-Growth on Substrate freie Oberfläche Interface-Tracking Induktion metallurgische MHD MHD Magnetodynamik Hydrodynamik Thermodynamik Magnetohydrodynamik OpenFOAM foam-extend Methodenentwicklung Softwareplattform Numerische Methoden Strömung mit freier Oberfläche Metalle Halbmetalle Silizium Wafer 3D METIS FVM Finite-Volumen-Methode elektromagnetische Wechselfelder zeitharmonische Anregung Frequenzraum Blockmatrizen diskontinuierliche Materialeigenschaften magnetische Permeabilität elektrische Leitfähigkeit eingebettete Diskretisierung GFM Ghost-Fluid-Methode Mehrfeldproblem Multi-Physics Biot-Savart Biot-Savart-Gesetz Biot-Savart-Induktoren überlagerte Gitter ALE Gitterbewegung Kopplung FAM Finite-Flächen-Methode RMF rotierendes Magnetfeld TMF wanderndes Magnetfeld Validierung Maxwell Maxwell-Gleichungen Navier-Stokes Navier-Stokes-Gleichung inkompressibel Schmelze Lorentz-Kraft Induktor Konduktor Induktionsspulen Wirbelströme Wirbelstromproblem PISO Oberflächenspannung semi-gekoppelter Lösungsalgorithmus Diskretisierung Skineffekt AC quasistatische Approximation Magneto-Quasistatik metallurgy crystal growth electromagnetic processing optimization Simulation RGS Ribbon-Growth on Substrate free-surface interface-tracking Induction metallurgical MHD MHD magnetodynamics hydrodynamics thermodynamics magnetohydrodynamics OpenFOAM foam-extend method development software platform numerical methods free-surface flow metals metalloids silicon wafer 3D METIS FVM Finite-Volumen-Method oscillating magnetic fields time-harmonic excitation frequency domain block-matrices discontinuous material properties magnetic permeability electrical conductivity embedded discretization GFM Ghost-Fluid-Method multi-physics Biot-Savart Biot-Savart-inductor overlapped meshes ALE mesh movement coupling FAM Finite-Area-Method RMF rotating magnetic field TMF traveling magnetic field validation Maxwell Maxwell-equations Navier-Stokes Navier-Stokes-equation incompressible melt melt flow Lorentz-force inductor conductor induction coil eddy-currents eddy-current problem PISO surface-tension semi-coupled solution discretization skin effect AC quasi-static approximation ddc:620 rvk:UF 4600
5	Methodenentwicklung zur Simulation von Strömungen mit freier Oberfläche unter dem Einfluss elektromagnetischer Wechselfelder Beckstein, Pascal 08 January 2018 (has links) Im Bereich der industriellen Metallurgie und Kristallzüchtung treten bei zahlreichen Anwendungen, wo magnetische Wechselfelder zur induktiven Beeinflussung von leitfähigen Werkstoffen eingesetzt werden, auch Strömungen mit freier Oberfläche auf. Das Anwendungsspektrum reicht dabei vom einfachen Aufschmelzen eines Metalls in einem offenen Tiegel bis hin zur vollständigen Levitation. Auch der sogenannte RGS-Prozess, ein substratbasiertes Kristallisationsverfahren zur Herstellung siliziumbasierter Dünnschichtmaterialien, ist dafür ein Beispiel. Um bei solchen Prozessen die Interaktion von Magnetfeld und Strömung zu untersuchen, ist die numerische Simulationen ein wertvolles Hilfsmittel. Für beliebige dreidimensionale Probleme werden entsprechende Berechnungen bisher durch eine externe Kopplung kommerzieller Programme realisiert, die für Magnetfeld und Strömung jeweils unterschiedliche numerische Techniken nutzen. Diese Vorgehensweise ist jedoch im Allgemeinen mit unnötigem Rechenaufwand verbunden. In dieser Arbeit wird ein neu entwickelter Methodenapparat auf Basis der FVM vorgestellt, mit welchem sich diese Art von Berechnungen effizient durchführen lassen. Mit der Implementierung dieser Methoden in foam-extend, einer erweiterten Version der quelloffenen Software OpenFOAM, ist daraus ein leistungsfähiges Werkzeug in Form einer freien Simulationsplattform entstanden, welches sich durch einen modularen Aufbau leicht erweitern lässt. Mit dieser Plattform wurden in foam-extend auch erstmalig dreidimensionale Induktionsprozesse im Frequenzraum gelöst. info:eu-repo/classification/ddc/620 ddc:620

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