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Godunov-type algorithms for numerical modeling of solar plasma

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Języki publikacji
EN
Abstrakty
EN
We discuss numerical methods to solve the Cauchy problem for hyperbolic equations, paying attention to equations which describe physical phenomena in fluid dynamics. We concentrate on Godunov-type methods which adopt Riemann solvers. These methods constitute a formidable task due to complexity of hyperbolic equations. Despite this complexity we show that the Godunov-type methods can be successfully applied to simulate complex systems such as described by equations of magnetohydrodynamics. In particular, we simulate thermal mode in a two-dimensional x-point magnetic field topology that is embedded in a gravitationally stratified solar atmosphere.
Rocznik
Strony
35--56
Opis fizyczny
Bibliogr. 20 poz., wykr.
Twórcy
autor
autor
  • Faculty of Mathematics, Physics and Informatics, UMCS ul. Radziszewskiego 10, 20-031 Lublin, Poland
Bibliografia
  • Aschwanden, M.J. and Alexander, D. (2001) Flare Plasma Cooling from 30 MK down to 1 MK modeled from Yohkoh, GOES, and TRACE observations during the Bastille Day Event (14 July 2000). Solar Physics 204 (1/2), 91-120.
  • Brackbill, J.U. and Barnes, D.C. (1980) The effect of nonzero product of magnetic gradient and B on the numerical solution of the magnetohydrodynamic equations. J. Comp. Phys. 35, 426-430.
  • De Moortel, I. and Hood, A.W. (2003) The damping of slow MHD waves in solar coronal magnetic fields. Astronomy and Astrophysics 408, 755-765.
  • Field, G.B. (1965) Thermal Instability. Astrophysical Journal 142, 531-567.
  • Fryxell, B., Olson, K., Ricker, P., Timmes, F.X., Zingale, M., Truran, J.W., Lamb, D.Q., MacNeice, P., Rosner, R., and Tufo, H. (2000) FLASH: An Adaptive Mesh Hydrodynamics Code for Modeling Astrophysical Thermonuclear Flashes. The Astrophysical Journal Supplement Series 131 (1), 273-334.
  • Godunov, S.K. (1959) A difference scheme for numerical solution of discontinuous solution of hydrodynamic equations. Math. Sb. 47, 271-306.
  • Kolgan, V.P. (1972) Application of the minimum-derivative principle in the construction of finie-diverence schemes for numerical analysis of discontinuous solutions in gas dynamics. Uch. Zap. TsaGI 3 (6), 68-77.
  • Lee, D. and Deane, A.E. (2009) An unsplit staggered mesh scheme for multidimensional magnetohydrodynamics. J. Comput. Phys. 228 (4), 952-975.
  • LeVeque, R.J. (2002) Finite-Volume Methods for Hyperbolic Problems. Cambridge University Press, Cambridge.
  • McLaughlin, J.A., Hood, A.W. and De Moortel, I. (2011) MHD Wave Propagation Near Coronal Null Points of Magnetic Fields. Space Science Reviews 158 (2-4), 205-236.
  • Macnamara, C.K. and Roberts, B. (2010) Effects of thermal conduction and compressive viscosity on the period ratio of the slow mode. Astronomy and Astrophysics 515, 41-48.
  • MacNeice, P., Olson, K.M., Mobarry, C., de Fainchtein, R. and Packer, C. (2000) PARAMESH: A parallel adaptive mesh refinement community toolkit. Computer Physics Communications 126 (3), 330-354.
  • Mędrek,M., Murawski,K. and Nakariakov,V.M. (2000) Propagational Aspects of Sunquake Waves. Acta Astronomica 50, 405-416.
  • Murawski, K. (2002) Analytical and Numerical Methods for Wave Propagation in Fluids. World Scientific, Singapore.
  • Murawski, K. and Lee, D. (2011) Numerical methods of solving equations of hydrodynamics from perspectives of the code FLASH. Bull. the Polish Academy of Sc. 59, 81-92.
  • Powell, K.G. (1994) Approximate Riemann solver for magnetohydrodynamice (that works in more than one dimension). ICASE Report No. 94-24, Langley, VA.
  • Roe, P.L. (1981) Approximate Riemann solvers, parameter vectors and difference schemes. J. Comp. Phys. 43, 357-372.
  • Toro, E. (2009) Riemann Solvers and Numerical Methods for Fluid Dynamics. Springer, Berlin.
  • van Leer, B. (1979) Towards the ultimate conservative difference scheme. V -A secondo-order sequel to Godunov method. J. Comp. Phys. 32, 101-136.
  • von Neumann, J. and Richtmeyer, R.D. (1950) A method for the numerical calculation of hydrodynamic shocks. J. Appl. Phys. 21, 232-237.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BATC-0009-0036
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