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Summation By Part Methods for Poisson's Equation with Discontinuous Variable Coefficients
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology.
2014 (English)Independent thesis Advanced level (professional degree), 20 credits / 30 HE creditsStudent thesis
Abstract [en]

Nowadays there is an ever increasing demand to obtain more accurate numericalsimulation results while at the same time using fewer computations. One area withsuch a demand is oil reservoir simulations, which builds upon Poisson's equation withvariable coefficients (PEWVC). This thesis focuses on applying and testing a high ordernumerical scheme to solve the PEWVC, namely Summation By Parts - SimultaneousApproximation Term (SBP-SAT). The thesis opens with proving that the method isconvergent at arbitrary high orders given sufficiently smooth coefficients. Theconvergence is furthermore verified in practice by test cases on the Poisson'sequation with smoothly variable permeability coefficients. To balance observed lowerboundary flux convergence, the SBP-SAT method was modified with additionalpenalty terms that were subsequently shown to work as expected. Finally theSBP-SAT method was tested on a semi-realistic model of an oil reservoir withdiscontinuous permeability. The correctness of the resulting pressure distributionvaried and it was shown that flux leakage was the probable cause. Hence theproposed SBP-SAT method performs, as expected, very well in continuous settingsbut typically allows undesirable leakage in discontinuous settings. There are possiblefixes, but these are outside the scope of this thesis.

Place, publisher, year, edition, pages
2014. , 81 p.
UPTEC F, ISSN 1401-5757 ; 14040
Keyword [en]
SBP, SAT, Summation By Parts, Poisson equation, Discontinuous coefficients, Numerical methods, oil reservoir, improved boundary, weak boundary
National Category
Other Engineering and Technologies not elsewhere specified
URN: urn:nbn:se:uu:diva-235418OAI: diva2:760015
Subject / course
Computer Systems Sciences
Educational program
Master Programme in Engineering Physics
Available from: 2014-11-06 Created: 2014-11-02 Last updated: 2014-11-06Bibliographically approved

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