Modelling of the convective plasma dynamics in the Sun: anelastic and Boussinesq MHD systems
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This work deals with the mathematical modelling and asymptotic analysis of the plasma convective dynamics in the center of the Sun. The heat produced via thermonuclear fusion in the interior of the Sun is transported towards the surface first via radiation, and finally via convection. Convection is thought to be responsible for the generation of magnetic fields and is hence a very important phenomenon to be understood in detail in order to get more insight in the internal structure of the Sun. Anelastic and Boussinesq models are formally derived here from the underlying compressible MHD models and we shall prepare the ground for our future numerical works, based on asymptotic-preserving techniques.
KeywordsPlasma modelling Convection in the Sun Singularly perturbed problems Compressible MHD-system Anelastic equation Boussinesq equation Asymptotic-preserving scheme
Mathematics Subject Classification35C20 76X05
The author is grateful to Claudia Negulescu (Université Paul Sabatier, Toulouse) for having introduced him to the research field of AP schemes, and for sharing knowledge and ideas that led to this paper. This work was partially supported by the Italian National Group for Mathematical Physics (GNFM/INdAM). The author—well aware of his good fortune—would like to express his gratitude and deepest appreciation to Tommaso Ruggeri for being such a supportive, generous and invaluable one-of-a-kind mentor.
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