MHD modeling and numerical simulation with finite volume-type methods. Application to fusion plasma

Abstract : This work deals with the modeling of fusion plasma which is discussed by using a bi-temperature Euler model and the ideal and resistive magnetohydrodynamic (MHD) ones. First, these models are established from the bi-fluid MHD equations and we show that they correspond to different asymptotic regimes for lowly or highly magnetized plasma. Next, we describe the finite volume methods for structured and non-structured meshes which have been used to approximate the solution of these models. For the three mathematical models studied in this thesis, the numerical methods are based on relaxation schemes. In order to apply those methods to magnetic confinement fusion problems, we explain how to modify the finite volume methods to apply it to problem given in cylindrical coordinates while keeping a strong conservative formulation. Finally, a strategy dealing with the divergence-free constraint of the magnetic field is studied. A set of numerical tests for the three models is presented for different geometries to validate the proposed numerical methods.
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Élise Estibals. MHD modeling and numerical simulation with finite volume-type methods. Application to fusion plasma. General Mathematics [math.GM]. Université Côte d'Azur, 2017. English. ⟨NNT : 2017AZUR4023⟩. ⟨tel-01551701v2⟩

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