Modélisations fluides pour les plasmas de fusion : approximation par éléments finis C1 de Bell

Abstract : Fluid instabilities can degrade plasma confinement in tokamaks. Given the spatial and temporal scales, we choose the fluid models obtained from the derivation of kinetic models. We derived several hierarchical models of MagnetoHydroDynamic (MHD) and in particular models of reduced MHD like the Current Hole and the Grad-Shafranov equilibrium. One of the difficulty of all these models is to respect the absence of magnetic monopoles equation. To ensure this condition at any point, the magnetic field is rewritten with a vector potential. The use of vector portential implies that higher order derivatives appear in the equation. The numerical strategy is developed using the finite element method with C1 Bell's elements. On a unstructured mesh, these have the advantage to present a reduced basis with degrees of freedom defined exclusively on the nodes of the mesh. The reduced MHD models of the Current Hole and Grad-Shafranov have thus been resolved with these elements. The resolution of a Grad-Shafranov test case with exact boundary conditions yields the optimal order of 5. The resolution of the Current Hole system with thesse elements has been validated by obtaining physical parameter η1/3 and allowed the observation of the development of sawtooth instabilities.
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Marie Martin. Modélisations fluides pour les plasmas de fusion : approximation par éléments finis C1 de Bell. Mathématiques générales [math.GM]. Université Nice Sophia Antipolis, 2013. Français. ⟨NNT : 2013NICE4031⟩. ⟨tel-00845922⟩

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