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Analysis of the energy exchange between atmosphere and ground using the compressible Navier-Stokes equations and the heat equation
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing.
2016 (English)Independent thesis Advanced level (professional degree), 20 credits / 30 HE creditsStudent thesis
Abstract [en]

In this paper the interface between the one dimensional compressible Navier-Stokes equation and the heat equation is analysed. For the linearized and symmetrized model, the energy method is used to derive interface conditions that bounds the solution. First, the characteristic far field boundary conditions are derived for the Navier-Stokes equation, second boundary conditions for a solid wall are derived and last interface condition with a heat equation. High order Summation-by-Parts operators are used for the spatial discretization. Boundary and interface conditions are weakly imposed using Simultaneous Approximation Terms. The implementation is stable and the method of manufactured solution is used to verify the implementation. An efficiency study showed that high order operators are superior in how much computer power is needed to get an accurate solution. 

Place, publisher, year, edition, pages
UPTEC F, ISSN 1401-5757 ; 16052
National Category
Computational Mathematics
URN: urn:nbn:se:uu:diva-304006OAI: diva2:975124
External cooperation
Rossby Centre, Sveriges Meteorologiska och Hydrologiska Institut
Educational program
Master Programme in Engineering Physics
Available from: 2016-09-29 Created: 2016-09-28 Last updated: 2016-10-03Bibliographically approved

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