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Outflow boundary conditions for the Fourier transformed two-dimensional Vlasov equation
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis. Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Astronomy and Space Physics. (Waves and Fluids)
2002 (English)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 181, 98-125 p.Article in journal (Refereed) Published
Place, publisher, year, edition, pages
2002. Vol. 181, 98-125 p.
National Category
Computational Mathematics Computer Science
URN: urn:nbn:se:uu:diva-79492DOI: 10.1006/jcph.2002.7121OAI: oai:DiVA.org:uu-79492DiVA: diva2:107405
Available from: 2007-01-26 Created: 2007-01-26 Last updated: 2011-11-28Bibliographically approved
In thesis
1. Numerical Vlasov–Maxwell Modelling of Space Plasma
Open this publication in new window or tab >>Numerical Vlasov–Maxwell Modelling of Space Plasma
2002 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The Vlasov equation describes the evolution of the distribution function of particles in phase space (x,v), where the particles interact with long-range forces, but where shortrange "collisional" forces are neglected. A space plasma consists of low-mass electrically charged particles, and therefore the most important long-range forces acting in the plasma are the Lorentz forces created by electromagnetic fields.

What makes the numerical solution of the Vlasov equation a challenging task is that the fully three-dimensional problem leads to a partial differential equation in the six-dimensional phase space, plus time, making it hard even to store a discretised solution in a computer’s memory. Solutions to the Vlasov equation have also a tendency of becoming oscillatory in velocity space, due to free streaming terms (ballistic particles), in which steep gradients are created and problems of calculating the v (velocity) derivative of the function accurately increase with time.

In the present thesis, the numerical treatment is limited to one- and two-dimensional systems, leading to solutions in two- and four-dimensional phase space, respectively, plus time. The numerical method developed is based on the technique of Fourier transforming the Vlasov equation in velocity space and then solving the resulting equation, in which the small-scale information in velocity space is removed through outgoing wave boundary conditions in the Fourier transformed velocity space. The Maxwell equations are rewritten in a form which conserves the divergences of the electric and magnetic fields, by means of the Lorentz potentials. The resulting equations are solved numerically by high order methods, reducing the need for numerical over-sampling of the problem.

The algorithm has been implemented in Fortran 90, and the code for solving the one-dimensional Vlasov equation has been parallelised by the method of domain decomposition, and has been implemented using the Message Passing Interface (MPI) method. The code has been used to investigate linear and non-linear interaction between electromagnetic fields, plasma waves, and particles.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2002. 28 p.
Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1104-232X ; 758
Vlasov equation, Maxwell equation, Fourier method, outflow boundary, domain decomposition
National Category
Computational Mathematics
Research subject
Numerical Analysis
urn:nbn:se:uu:diva-2929 (URN)91-554-5427-5 (ISBN)
Public defence
2002-11-29, Room 2347, Polacksbacken, Uppsala University, Uppsala, 10:15 (English)
Available from: 2002-11-06 Created: 2002-11-06 Last updated: 2011-10-26Bibliographically approved

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