| 1. |
- Scheffel, Jan, 1954-, et al.
(författare)
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Introducing the Novatron, a novel reactor concept
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- A new magnetic mirror design is described – the Novatron – with the potential to confine fully stable compact mirror-cusp fusion plasmas. The novel design features an axisymmetric magnetic field configuration with concave curvature throughout, as seen from the outside. Moreover, the Novatron is designed to be self-stabilized against the drift cyclotron loss-cone modes (DCLC). This paper describes the fundamental topology of the magnetic field and presents an outline for the design of the magnet system.
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| 2. |
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| 3. |
- Arber, T. D., et al.
(författare)
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Large Larmor Radius Stability of the Z-pinch
- 1994
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Ingår i: Physical Review Letters. - 0031-9007 .- 1079-7114. ; 72, s. 2399-
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Tidskriftsartikel (refereegranskat)abstract
- The linear m=0 stability of the z pinch in the collisionless, large ion Larmor radius regime is examined using the Vlasov fluid model. The results reveal a strong equilibrium dependence. The uniform current density equilibrium shows a reduction in growth rate when the average ion Larmor radius is about one-fifth of the pinch radius. However, finite Larmor radius effects cannot in themselves produce a stabilized z pinch.
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| 4. |
- Arber, T. D., et al.
(författare)
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Linear Stability of the High Temperature, Dense Z-pinch
- 1995
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Ingår i: Physical Review Letters. - 0031-9007 .- 1079-7114. ; 74, s. 2698-
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Tidskriftsartikel (refereegranskat)abstract
- Results are presented on the linear stability of the collisionless m=1 mode in a dense Z pinch. It is shown that a reduction in growth rate by a factor of about 10 (when compared to the zero Larmor radius result) is possible by initializing the Z pinch with a sufficiently low line density. With the completion of this work we conclude that linear, large Larmor radius effects cannot stabilize the high temperature, dense Z pinch. Such pinches will always exhibit linear m=0 or m=1 instabilities with growth times comparable to the radial Alfvén transit time.
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| 5. |
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| 6. |
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| 7. |
- Brunsell, P., et al.
(författare)
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Extrap L-1 Experimental Stability
- 1990
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Ingår i: XVII European Conference on Controlled Fusion and Plasma Heating, Amsterdam, Netherlands, June 25-29, 1990. ; , s. 610-
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Konferensbidrag (refereegranskat)
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| 8. |
- Brunsell, Per R., et al.
(författare)
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Mode Dynamics and Confinement in the Reversed-field Pinch
- 2000
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Ingår i: 18<sup>th</sup> IAEA Fusion Energy Conference in Sorrento, Italy, 4-10 Oct. 2000. Paper IAEA-CN-77/EXP3/14.
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Konferensbidrag (refereegranskat)abstract
- Tearing mode dynamics and toroidal plasma flow in the RFP has been experimentally studied in the Extrap T2 device. A toroidally localised, stationary magnetic field perturbation, the ``slinky mode'' is formed in nearly all discharges. There is a tendency of increased phase alignment of different toroidal Fourier modes, resulting in higher localised mode amplitudes, with higher magnetic fluctuation level. The fluctuation level increases slightly with increasing plasma current and plasma density. The toroidal plasma flow velocity and the ion temperature has been measured with Doppler spectroscopy. Both the toroidal plasma velocity and the ion temperature clearly increase with I/N. Initial, preliminary experimental results obtained very recently after a complete change of the Extrap T2 front-end system (first wall, shell, TF coil), show that an operational window with mode rotation most likely exists in the rebuilt device, in contrast to the earlier case discussed above. A numerical code DEBSP has been developed to simulate the behaviour of RFP confinement in realistic geometry, including essential transport physics. Resulting scaling laws are presented and compared with results from Extrap T2 and other RFP experiments.
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| 9. |
- Coppins, M., et al.
(författare)
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Anisotropic Z-Pinch Equilibria and Their Stability
- 1992
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Ingår i: Physics of fluids. - : AIP Publishing. - 1070-6631 .- 1089-7666. ; B4, s. 3251-
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Tidskriftsartikel (refereegranskat)abstract
- The Chew–Goldberger–Low equations are used to study the effect of pressure anisotropy on Z‐pinches operating in the collisionless regime. The limitations on the form of accessible equilibria are investigated. The effect on the m=0 instability is asessed both by means of the energy principle and by direct solution of the eigenvalue equation for a variety of anisotropicequilibria. The results indicate that in the small Larmor radius limit pressure anisotropy offers a rather slight enhancement of the linear stability of the Z‐pinch.
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| 10. |
- Coppins, M., et al.
(författare)
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CGL Anisotropic Equilibria and Stability
- 1989
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Ingår i: 2nd International Conference on High Density Pinches, Laguna Beach, CA, USA 1989. ; , s. 211-
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Konferensbidrag (refereegranskat)
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| 11. |
- Coppins, M., et al.
(författare)
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FIGARO-a Large Larmor Radius Stability Code
- 1992
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Ingår i: International Conference on Plasma Physics, Innsbruck, Austria, 29 June - 3 July, 1992. ; , s. 663-
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Konferensbidrag (refereegranskat)
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| 12. |
- Coppins, M., et al.
(författare)
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Recent progress on large Larmor radius theory
- 1997
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Ingår i: Fourth International Conference on Dense Z-pinches, Vancouver, Canada, 28-31 May 1997. - : ASCE. ; , s. 585-
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Konferensbidrag (refereegranskat)abstract
- An overview of theoretical work on large Larmor radius stability of the z-pinch is presented, highlighting two recent innovations. Firstly, finite electron temperature has been included for the linear m=0 instability. Compared to the usual cold electron case, growth rates are increased and are closer to those of ideal MHD. Secondly, a 2-D hybrid code has been written to study the non-linear development of the m=0 instability. First results provide no evidence of instability saturation.
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| 13. |
- Dahlin, Jon-Erik, 1977-, et al.
(författare)
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Advanced Reversed-field Pinch Scaling Laws
- 2005
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Ingår i: 32nd EPS Conference on Plasma Physics, Tarragona, Spain 27 June-1 July, P-1.118, 2005.
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Konferensbidrag (refereegranskat)abstract
- A series of resistive magnetohydrodynamic numerical simulations are performed to generate scaling laws for energy confinement time τE and poloidal beta βp for the advanced reversed field-pinch (RFP). Strongly improved scaling with basic initial parameters is obtained as compared to the conventional RFP. Early results indicate an improved scaling of τE with plasma current I and line density N compared to the conventional RFP. The improved behaviour of the advanced RFP as compared to the conventional, uncontrolled RFP stems from the introduction of current profile control (CPC). In the present numerical simulations, CPC is performed by implementation of a parameter free automatic feedback algorithm, optimised to reduce the fluctuation caused v × B electric field. The scheme introduces an ad-hoc electric field within the plasma volume, automatically adjusted to dynamically control the plasma into more quiescent behaviour by eliminating current driven tearing mode instabilities and reducing resistive interchange modes.
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| 14. |
- Dahlin, Jon-Erik, 1977-, et al.
(författare)
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Improved Computer Simulations of Energy Confinement in the Advanced Reversed-field Pinch
- 2006
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Ingår i: 33rd EPS Conference on Plasma Phys. - 9781622763337
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Konferensbidrag (refereegranskat)abstract
- A revised algorithm for numerical simulations of the advanced reversed-field pinch (RFP) is presented. The results show improved scalings of magnetic fluctuations, energy confinement time τE and poloidal beta βθ with basic initial parameters as compared to what has been presented by the authors in earlier studies of the advanced RFP. The improved behaviour of the advanced RFP stems from the introduction of current profile control (CPC), implemented through a scheme of active feedback of the electric dynamo field. The work, which has an optimistic approach and sweeps over a large parameter domain reaching into the reactor relevant region, is theoretical and claims to answer the question of how far CPC can bring the RFP concept in principle. Experimental implementation is thus a later concern. With this scheme, a state with strongly suppressed tearing mode activity is achieved, which allows for a theoretical study of pressure driven resistive g-modes. This is a task that has been very hard to perform in the past, since tearing modes have always dominated the RFP dynamics. Thus it is now possible, for the first time, to investigate whether pressure driven modes, which are persistent in the RFP, are fatal for the confinement of a high-beta RFP configuration or if they can be accepted in a future reactor.
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| 15. |
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| 16. |
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| 17. |
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| 18. |
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| 19. |
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| 20. |
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| 21. |
- Elevant, T., et al.
(författare)
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Profile Measurements in ITER by means of Neutron Spectroscopy, Ion Temperature Diagnostics for Experimental Thermonuclear Fusion Reactors
- 1996
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Ingår i: Workshop on diagnostics for ITER, Varenna, September 1995, proceedings of the International School of Plasma Physics, Edited by P. E. Stott et.al., Plenum Press, New York, 1996. - Boston, MA : Springer US. ; , s. 445-450
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Konferensbidrag (refereegranskat)abstract
- Information on ion temperature profiles will be needed for burn optimisation and transport studies in ITER. The feasibility of deriving these profiles for the core plasma (r< 0.75a) directly from the width of measured 14-MeV neutron energy spectra is demonstrated for Maxwellian ion distributions. Neutron energy spectra and fluxes generated under different heating conditions are calculated by means of Monte-Carlo technique. The computation takes the reaction kinematics and the velocity distributions of the reacting ions into account and calculates the resulting neutron energy distribution and flux into a defined collimator. Energy spectra of neutrons emitted along a line-of-sight are superimposed. The associated correction factor, which depends on the measured ion temperature, can be given an analytical form when fitted to code data and is insensitive to large variations in temperature-, density and magnetic flux profile shapes. The accuracy in ion temperature evaluation is expected to be better than ± 10% and can be improved to ± 5% provided information on fuel density profiles are made available.
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| 22. |
- Elevant, T., et al.
(författare)
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Role of Neutron Spectrometers for ITER
- 1998
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Ingår i: Proc. of the Int. School of Plasma Physics "Piero Calderola", Workshop on Diagnostics for Experimental Fusion Reactors, held September 4-12, 1997, in Varenna, Italy. Edited by Stott et al, Plenum Press, New York, 1998.
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Konferensbidrag (refereegranskat)abstract
- Conditions for retrieval of ion temperature profiles through measurement and evaluation of neutron energy spectra emitted in ITER-like fusion plasmas are discussed. Spectra from deuterium- and deuterium-tritium plasmas heated by 100 MW, 1 MeV neutral deuterium beams, and ignited H-mode plasmas are simulated by means of a Monte-Carlo Fokker-Planck code. Regions are defined where information on ion temperature clearly is preserved. The correction from line-of-sight integrated measurement to peak temperature is found to be 4–10% for deuterium plasmas of all temperatures and for deuterium-tritium plasmas of temperatures below approximately 5 keV. For higher temperatures the correction equals 10–30% depending on the density and temperature profiles. Ion temperatures can be determined with an accuracy better than 10% in this region only if profile data is made available.Several spectrometers have been proposed. Operating ranges in ion temperature and beam power, spatial- and temporal resolution, space requirements and life expectancy are compared with ITER measurement requirements. Necessary R&D work is also discussed.
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| 23. |
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| 24. |
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| 25. |
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| 26. |
- Faghihi, M., et al.
(författare)
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Stability of Small Axial Wavelength Internal Kink Modes of an Anisotropic Plasma
- 1987
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Ingår i: Journal of Plasma Physics. - 0022-3778 .- 1469-7807. ; 38, s. 495-
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Tidskriftsartikel (refereegranskat)abstract
- The double adiabatic equations are used to study the stability of a cylindrical Z-pinch with respect to small axial wavelength, internal kink (m ≥ 1) modes. It is found that marginally (ideally) unstable, isotropic equilibria are stabilized. Also, constant-current-density equilibria can be stabilized for P⊥ > P∥ and large β⊥
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| 27. |
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| 28. |
- Frassinetti, Lorenzo, et al.
(författare)
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Vektoranalys
- 2019. - 1
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Bok (refereegranskat)abstract
- Läroböcker i vektoranalys är ofta kortfattade. Denna bok, som kan användas för såväl grundläggande som mer avancerade kurser, behandlar ämnet mer utförligt.Bokens pedagogiska idé skiljer sig markant från liknande böcker. Återkommande inslag är tydligt formulerade problem som fångar det centrala i vektoranalysen. Syftet med problemen är dels att väcka intresse för den teori och de metoder som behandlas, dels att stimulera till aktivt lärande. Boken innehåller genomarbetade och lättillgängliga teoriavsnitt - som börjar med grundläggande vektoralgebra och slutar med kartesiska tensorer och en härledning av vektoranalysens huvudsats. Dessutom ingår ett stort antal konkreta exempel och många tillämpningar. Sist i varje kapitel finns en sammanfattning av den viktigaste teorin och övningsuppgifter med svar. Ledningar och fullständiga lösningar finns på Libers webbplats. Där finns även ett Appendix med tillämpningar.
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| 29. |
- Haines, M. G., et al.
(författare)
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Fiber Z-pinch Experiments and Calculations in the Finite Larmor Radius Regime
- 1996
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Ingår i: Laser and particle beams (Print). - 0263-0346 .- 1469-803X. ; 14, s. 261-271
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Tidskriftsartikel (refereegranskat)abstract
- The dense Z-pinch project at Imperial College is aimed at achieving radiative collapse to high density in a hydrogen plasma, and also to study plasmas close to controlled fusion conditions. To this end, the MAGPIE generator (2.4 MV, 1.25, and 200 ns) has been built and tested, and is now giving preliminary experimental data at 60% of full voltage for carbon and CD2 fibers. These discharges are characterized by an initial radial expansion followed by the occurrence of m = 0 structures with transient X-ray emission from bright spots. Late in the discharge a disruption can occur, accompanied by hard X-ray emission from the anode due to an energetic electron beam and, in the case of CD2 fibers, a neutron burst. Concomitant theoretical studies have solved the linear stability problem for a Z-pinch with large ion Larmor radii, showing that a reduction in growth rate of m = 0 and m = 1 modes to about 20% of the magnetohydrodynamic (MHD) value can occur for a parabolic density profile when the Larmor radius is optimally 20% of the pinch radius. Two dimensional MHD simulations of Z-pinches in two extremes of focussed short-pulse laserplasma interactions and of galactic jets reveal a nonlinear stabilizing effect in the presence of sheared flow. One-dimensional simulations show that at low line density the lower hybrid drift instability can lead to coronal radial expansion of a Z-pinch plasma.
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| 30. |
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| 31. |
- Hellsten, Torbjörn, et al.
(författare)
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Continuous Double Adiabatic Spectrum in Toroidal Plasmas
- 1984
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Ingår i: Physica Scripta. - 0031-8949 .- 1402-4896. ; 30, s. 78-
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Tidskriftsartikel (refereegranskat)abstract
- The continuous spectrum of an anisotropic and axisymmetric toroidal plasma is investigated using the double adiabatic theory. The continuum is given by an eigenvalue problem of a fourth order system of ordinary differential equations. In contrast to the magnetohydrodynamic continuum the double adiabatic continuum may become unstable. The stability depends upon the parallel and perpendicular pressure distributions along the field lines. In absence of a toroidal magnetic field, the fourth order system decouples into two second order differential equations for which specific stability criteria are derived.
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| 32. |
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| 33. |
- Lehnert, B., et al.
(författare)
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Comments on the Theory of the Rayleigh-Taylor Instability in the Limit of Large Larmor Radii
- 1988
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Ingår i: Physical Review Letters. - 0031-9007 .- 1079-7114. ; 61, s. 897-
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Tidskriftsartikel (refereegranskat)abstract
- In recent investigations Hassam and Huba as well as Huba, Lyon, and Hassam have reconsidered the theory on the Rayleigh-Taylor flute-type instability in the limit of large Larmor radius. They have performed a numerical simulation starting from a set of modified MHD equations. The deductions made by the authors on the basis of these equations seem consistent. However, the MHD equations themselves are inconsistent, making the resulting conclusions questionable indeed.
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| 34. |
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| 35. |
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| 36. |
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| 37. |
- Lehnert, B., et al.
(författare)
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Parameter Limits of Screw-Pinch Equilibria
- 1992
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Ingår i: Plasma Physics and Controlled Fusion. - 0741-3335 .- 1361-6587. ; 34, s. 1113-1131
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Tidskriftsartikel (refereegranskat)abstract
- Anisotropic resistivity causes paramagnetic effects (Bz´(r) < 0) in a screw pinch, being basically different to the self-relaxation in reversed field-pinches. We compute, analytically and numerically, the resulting influence on the plasma radius and on plasma beta in a straight cylindrical plasma. The results seem to indicate that D-D screw-pinch reactors which depend on safety factors q(a) > 1 are unattainable. Diamagnetism caused by radial particle diffusion and the Nernst effect is also discussed. In a Tokamak or reactor plasma, diamagnetism is shown to be negligible, whereas it may contribute in present ultra-low q, Extrap and RFP experiments.A basic relation is derived for the coupling betwecn the poloidal and axial magnetic field components with the above effects included. Of specific importance to the Extrap programme is the result that plasma current limitation can arise due to the lack equilibrium when the plasma radius tends to exceed its upper limit, which is defined by a magnetic or material limiter. Comparisons are made with stability limits depending on the safety factor, the number of contained ion Larmor radii and the line density.
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| 38. |
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| 39. |
- Li., J., et al.
(författare)
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Boundary Larmor Radius Effect on Electrostatic Waves
- 1991
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Ingår i: Physics of fluids. - : AIP Publishing. - 1070-6631 .- 1089-7666. ; B3, s. 3013-
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Tidskriftsartikel (refereegranskat)abstract
- The linearized Vlasov–Poisson equations, which combine to an integrodifferential equation for the perturbed electric potential, are used to investigate the effect of finite plasma size on the stability of electrostatic waves in a homogeneous plasma slab. The distortion of the gyromotion of the particles at the plasma boundary influences wave stability, a phenomenon termed the boundary Larmor radius (BLR) effect. The integrodifferential equation, treated as an eigenvalue problem, is discretized into a matrix dispersion equation by use of the Galerkin method and is then solved numerically. It is found that the ion Bernstein wave,which is undamped in an infinite homogeneous plasma, now becomes damped with a maximum damping rate of 0.35 ωci at rG/L (ion Larmor radius over wall distance)≊0.15. In general, the damping is less pronounced at shorter perpendicular wavelengths. It implies a necessity to take into account the BLR effect in the kinetic stability studies for sufficiently large ion Larmor radius in comparison to the characteristic dimension.
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| 40. |
- Li, J., et al.
(författare)
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Boundary Larmor Radius Effects
- 1990
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Ingår i: XVII European Conference on Controlled Fusion and Plasma Heating, Amsterdam, Netherlands, June 25-29, 1990. ; , s. 1836-
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Konferensbidrag (refereegranskat)
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| 41. |
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| 42. |
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| 43. |
- Li, J., et al.
(författare)
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Kinetic High-beta Equilibria and Stability in a Plasma Slab
- 1991
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Ingår i: Physics of fluids. - : AIP Publishing. - 1070-6631 .- 1089-7666. ; B3, s. 2506-
-
Tidskriftsartikel (refereegranskat)abstract
- Self‐consistent, high‐beta kinetic equilibria are derived from the Vlasov equation for a plasma slab in a nonzero magnetic field with a density gradient and a gravitational field. It is shown that a magnetic field inhomogeneity and an electric field arise as necessary consequences of the high‐beta state. Hence the corresponding equilibrium forces should not be neglected in calculations of individual particle motion. Explicit expressions are derived for equilibrium quantities, useful, e.g., for large Larmor radius (LLR) studies of the Rayleigh–Taylor instability.
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| 44. |
- Lindvall, Kristoffer, 1990-, et al.
(författare)
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Can the Time-Spectral Method GWRM Advance Fusion Transport Modelling?
- 2017
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Ingår i: 59th Annual Meeting of the APS Division of Plasma Physics.
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Konferensbidrag (refereegranskat)abstract
- Transport phenomena in fusion plasma pose a daunting task for both real-time experiments and numerical modelling. The transport is driven by micro-instabilities caused by a host of unstable modes, for example ion temperature gradient and trapped electron modes. These modes can be modelled using fluid or gyrokinetic equations. However, the equations are characterised by high degrees of freedom and high temporal and spatial numerical requirements. Thus, a time-spectral method GWRM has been developed in order to efficiently solve these multiple time scale equations. The GWRM assumes a multivariate Chebyshev expansion ansatz in time, space, and parameter domain. Advantages are that time constraining CFL criteria no longer apply and that the solution accurately averages over small time-scale dynamics. For benchmarking, a two-fluid 2D drift wave turbulence model has been solved in order to study toroidal ion temperature gradient growth rates and nonlinear behaviour.
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| 45. |
- Lindvall, Kristoffer, 1990-, et al.
(författare)
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Spectral Representation of Time and Physical Parameters in Numerical Weather Prediction
- 2018
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Ingår i: Understanding of Atmospheric Systems with Efficient Numerical Methods for Observation and Prediction. - : IntechOpen.
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Bokkapitel (refereegranskat)abstract
- Numerical weather prediction (NWP) is a difficult task in chaotic dynamical regimes because of the strong sensitivity to initial conditions and physical parameters. As a result, high numerical accuracy is usually necessary. In this chapter, an accurate and efficient alternative to the traditional time stepping solution methods is presented; the time-spectral method. The generalized weighted residual method (GWRM) solves systems of nonlinear ODEs and PDEs using a spectral representation of time. Not being subject to CFL-like criteria, the GWRM typically employs time intervals two orders of magnitude larger than those of time-stepping methods. As an example, efficient solution of the chaotic Lorenz 1984 equations is demonstrated. The results indicate that the method has strong potential for NWP. Furthermore, employing spectral representations of physical parameters and initial values, families of solutions are obtained in a single computation. Thus, the GWRM is conveniently used for studies of system parameter dependency and initial condition error growth in NWP.
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| 46. |
- Lindvall, Kristoffer
(författare)
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Time Spectral Methods - Towards Plasma Turbulence Modelling
- 2021
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Energy comes in two forms; potential energy and kinetic energy. Energyis stored as potential energy and released in the form of kinetic energy. This process of storage and release is the basic strategy of all energy alternatives in use today. This applies to solar, wind, fossil fuels, and the list goes on. Most of these come in diluted and scarce forms allowing only a portion of the energy to be used, which has prompted the quest for the original source, the Sun.As early as 1905 in the work by Albert Einstein on the connection between mass and energy, it has been seen theoretically that energy can be extracted from the process of fusing lighter elements into heavier elements. Later, this process of fusion was discovered to be the very source powering the Sun. Almost a century later, the work continues to make thermonuclear fusion energy a reality.Looking closer at the Sun, we see that it consists of a hot burning gas subject to electromagnetic fields, i.e. a plasma. The plasma in the Sun is contained by the massive gravitational force which allows for fusion to be created in a stable and continuous process. Taking inspiration from the Sun we see that a hot plasma and its containment are key to achieving fusion. The gravitational force is not present on Earth, and creating it artificially is, a sof today, an insurmountable task. Fortunately, the plasma can be contained in another way; with magnetic fields.The challenges of making fusion a viable energy source are numerous and diverse. To deal with these challenges there are several fields of fusion research; engineering, physics, and numerical analysis. These of course overlap, but serve to illustrate the focus of different groups. This thesis work is focused on the latter two, physics and numerical analysis.The containment of the plasma in a fusion device is degraded by drift wave turbulence. The turbulence in the plasma occurs on the micro-scale, namely on the scale of particles travelling around the magnetic field lines. The physics behind turbulence and the drift waves responsible is a rich field with many future topics.Since the micro-turbulence can quickly grow and diffuse plasma throughout the device in a matter of micro-seconds, it becomes a difficult challenge to numerically resolve the turbulence over a longer span of time. The typical confinement times required in a fusion device is on the order of several seconds. Thus, the main focus of this thesis is on developing a numerical method that can effectively resolve the plasma physics over longer time-intervals. To this effect, a Time-Spectral method has been developed that utilizes the advantageous properties of spectral methods to all domains, specifically the temporal domain. The numerical method has been implemented on compressible Navier-Stokes, ideal magnetohydrodynamics (MHD), and a toroidal two-fluid plasma turbulence model called the Weiland model.
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| 47. |
- Lindvalll, Kristoffer, et al.
(författare)
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2D continuous Chebyshev-Galerkin time-spectral method
- 2022
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Ingår i: Computer Physics Communications. - : Elsevier BV. - 0010-4655 .- 1879-2944. ; 271, s. 108217-108217
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Tidskriftsartikel (refereegranskat)abstract
- A fully spectral multi-domain method has been developed and applied to three applications within ideal MHD, compressible Navier-Stokes, and a two-fluid plasma turbulence model named the Weiland model. The time-spectral method employed is the Generalized Weighted Residual Method (GWRM), where all domains such as space, time, and parameter space are spectrally decomposed with Chebyshev polynomials. The spectral decomposition of the temporal domain allows the GWRM to reach spectral accuracy in all dimensions. The GWRM linear/nonlinear algebraic equations are solved using an Anderson Acceleration (AA) method and a newly developed Quasi Semi-Implicit root solver (Q-SIR). Up to 85% improved convergence rate was obtained for Q-SIR as compared to AA and in certain cases only Q-SIR converged. In the most challenging simulations, featuring steep gradients, the GWRM converged for time intervals roughly two times larger than typical time steps for explicit time-marching schemes, being limited by the CFL condition. Time intervals up to 70 times larger than those of explicit time-marching schemes were used in smooth regions. Furthermore, the most computationally expensive algorithm, namely the product of two Chebyshev series, has been GPU accelerated with speedup gains of several thousands compared to a CPU.
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| 48. |
- Lindvalll, Kristoffer, et al.
(författare)
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A time-spectral method for initial-value problems using a novel spatial subdomain scheme
- 2018
-
Ingår i: Cogent Mathematics & Statistics. - : Informa UK Limited. - 2331-1835 .- 2574-2558. ; 5:1
-
Tidskriftsartikel (refereegranskat)abstract
- We analyse a novel subdomain scheme for time-spectral solution of initial-value partial differential equations. In numerical modelling spectral methods are commonplace for spatially dependent systems, whereas finite difference schemes are typically applied for the temporal domain. The Generalized Weighted Residual Method (GWRM) is a fully spectral method that spectrally decomposes all specified domains, including the temporal domain, using multivariate Chebyshev polynomials. The Common Boundary-Condition method (CBC) here proposed is a spatial subdomain scheme for the GWRM. It solves the physical equations independently from the global connection of subdomains in order to reduce the total number of modes. Thus, it is a condensation procedure in the spatial domain that allows for a simultaneous global temporal solution. It is here evaluated against the finite difference methods of Crank-Nicolson and Lax-Wendroff for two example linear PDEs. The CBC-GWRM is also applied to the linearised ideal magnetohydrodynamic (MHD) equations for a screw pinch equilibrium. The growth rate of the most unstable mode was efficiently computed with an error <0.1%.
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| 49. |
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| 50. |
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