期刊
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS
卷 96, 期 2, 页码 209-230出版社
WILEY
DOI: 10.1002/fld.5241
关键词
alternating Schwarz method; composite meshes; Hermite-Bezier finite elements; isoparametric finite elements; reduced Hsieh-Clough-Tocher finite elements
Finite elements of class C-1 are used for computing magnetohydrodynamics instabilities in tokamak plasmas, and isoparametric approximations are employed to align the mesh with the magnetic field line. This numerical framework helps in understanding the operation of existing devices and predicting optimal strategies for the international ITER tokamak. However, a mesh-aligned isoparametric representation encounters issues near critical points of the magnetic field, which can be addressed by combining aligned and unaligned meshes.
Finite elements of class C-1 are suitable for the computation of magnetohydrodynamics instabilities in tokamak plasmas. In addition, isoparametric approximations allow for a precise alignment of the mesh with the magnetic field line. Mesh alignment is crucial to achieve axisymmetric equilibria accurately. It is also helpful to deal with the anisotropy nature of magnetized plasma flows. In this numerical framework, several practical simulations are now available. They help to understand better the operation of existing devices and predict the optimal strategies for using the international ITER tokamak under construction. However, a mesh-aligned isoparametric representation suffers from the presence of critical points of the magnetic field (magnetic axis, X-point). We here explore a strategy that combines aligned mesh out of the critical points with non-aligned unstructured mesh in a region containing these points. By this strategy, we can avoid highly stretched elements and the numerical difficulties that come with them. The mesh-aligned interpolation uses bi-cubic Hemite-Bezier polynomials on a structured mesh of curved quadrangular elements. On the other hand, we assume reduced cubic Hsieh-Clough-Tocher finite elements on an unstructured triangular mesh. Both meshes overlap, and the resulting formulation is a coupled discrete problem solved iteratively by a suitable one-level Schwarz algorithm. In this paper, we will focus on the Poisson problem on a two-dimensional bounded regular domain. This elliptic equation is a simplified version of the axisymmetric tokamak equilibrium one at the asymptotic limit of infinite major radius (large aspect ratio).
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