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High accuracy mantle convection simulation through modern numerical methods
Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för beräkningsvetenskap. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
2012 (Engelska)Ingår i: Geophysical Journal International, ISSN 0956-540X, E-ISSN 1365-246X, Vol. 191, s. 12-29Artikel i tidskrift (Refereegranskat) Published
Ort, förlag, år, upplaga, sidor
2012. Vol. 191, s. 12-29
Nationell ämneskategori
Beräkningsmatematik Datavetenskap (datalogi)
Identifikatorer
URN: urn:nbn:se:uu:diva-162213DOI: 10.1111/j.1365-246X.2012.05609.xISI: 000308636800002OAI: oai:DiVA.org:uu-162213DiVA, id: diva2:459645
Tillgänglig från: 2012-08-21 Skapad: 2011-11-27 Senast uppdaterad: 2018-01-12Bibliografiskt granskad
Ingår i avhandling
1. Computational Techniques for Coupled Flow-Transport Problems
Öppna denna publikation i ny flik eller fönster >>Computational Techniques for Coupled Flow-Transport Problems
2011 (Engelska)Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
Abstract [en]

This thesis presents numerical techniques for solving problems of incompressible flow coupled to scalar transport equations using finite element discretizations in space. The two applications considered in this thesis are multi-phase flow, modeled by level set or phase field methods, and planetary mantle convection based on the Boussinesq approximation.

A systematic numerical study of approximation errors in evaluating the surface tension in finite element models for two-phase flow is presented. Forces constructed from a gradient in the same discrete function space as used for the pressure are shown to give the best performance. Moreover, two approaches for introducing contact line dynamics into level set methods are proposed. Firstly, a multiscale approach extracts a slip velocity from a micro simulation based on the phase field method and imposes it as a boundary condition in the macro model. This multiscale method is shown to provide an efficient model for the simulation of contact-line driven flow. The second approach combines a level set method based on a smoothed color function with a the phase field method in different parts of the domain. Away from contact lines, the additional information in phase field models is not necessary and it is disabled from the equations by a switch function. An in-depth convergence study is performed in order to quantify the benefits from this combination. Also, the resulting hybrid method is shown to satisfy an a priori energy estimate.

For the simulation of mantle convection, an implementation framework based on modern finite element and solver packages is presented. The framework is capable of running on today's large computing clusters with thousands of processors. All parts in the solution chain, from mesh adaptation over assembly to the solution of linear systems, are done in a fully distributed way. These tools are used for a parallel solver that combines higher order time and space discretizations. For treating the convection-dominated temperature equation, an advanced stabilization technique based on an artificial viscosity is used.

For more efficient evaluation of finite element operators in iterative methods, a matrix-free implementation built on cell-based quadrature is proposed. We obtain remarkable speedups over sparse matrix-vector products for many finite elements which are of practical interest. Our approach is particularly efficient for systems of differential equations.

Ort, förlag, år, upplaga, sidor
Uppsala: Acta Universitatis Upsaliensis, 2011. s. 61
Serie
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 885
Nyckelord
Finite element method, saddle point systems, two-phase flow, level set method, phase field method, stabilization, contact line dynamics
Nationell ämneskategori
Beräkningsmatematik Programvaruteknik
Forskningsämne
Beräkningsvetenskap med inriktning mot numerisk analys
Identifikatorer
urn:nbn:se:uu:diva-162215 (URN)978-91-554-8232-9 (ISBN)
Disputation
2012-01-13, Room 2446, Polacksbacken, Lägerhyddsvägen 2D, Uppsala, 14:00 (Engelska)
Opponent
Handledare
Tillgänglig från: 2011-12-20 Skapad: 2011-11-27 Senast uppdaterad: 2018-01-12Bibliografiskt granskad

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