Abstract In this work we present a hybrid discontinuous Galerkin scheme for the solution of extremely anisotropic diffusion problems arising in magnetized plasmas for fusion applications. Unstructured meshes, non-aligned with respect to the dominant diffusion direction, allow an unequalled flexibility in discretizing geometries of any shape, but may lead to spurious numerical diffusion. Curved triangles or quadrangles are used to discretize the poloidal plane of the machine, while a structured discretization is used in the toroidal direction. The proper design of the numerical fluxes guarantees the correct convergence order at any anisotropy level. Computations performed on well-designed 2D and 3D numerical tests show that non-aligned discretizations are able to provide spurious diffusion free solutions as long as high-order interpolations are used. Introducing an explicit measure of the numerical diffusion, a careful investigation is carried out showing an exponential increase of this latest with respect to the non-alignment of the mesh with the diffusion direction, as well as an exponential decrease with the polynomial degree of interpolation. A brief assessment of the method with respect to two finite-difference schemes using non-aligned discretization, but classically used in fusion modeling, is also presented. Program summary Program Title: Laplace-HDG (Laplace Hybrid Discontinuous Galerkin) CPC Library link to program files: http://dx.doi.org/10.17632/c3dhycyvj8.1 Licensing provisions: GPLv3 Programming language: Fortran 95 Nature of problem: Anisotropic Laplace problem in 2D with Dirichlet boundary conditions Solution method: Hybrid discontinuous Galerkin scheme

中文翻译：

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磁聚变中强各向异性扩散算子离散化的高阶非场对齐方法

摘要 在这项工作中，我们提出了一种混合不连续伽辽金方案，用于解决聚变应用中磁化等离子体中出现的极端各向异性扩散问题。非结构化网格与主要扩散方向不对齐，在离散任何形状的几何图形方面具有无与伦比的灵活性，但可能会导致虚假的数值扩散。弯曲的三角形或四边形用于离散化机器的极向平面，而结构化离散化用于环形方向。数值通量的正确设计保证了在任何各向异性水平上的正确收敛顺序。在精心设计的 2D 和 3D 数值测试上执行的计算表明，只要使用高阶插值，非对齐离散化就能够提供无伪扩散的解决方案。引入数值扩散的显式测量，进行了仔细研究，显示最近的网格与扩散方向的非对齐呈指数增长，以及随插值的多项式次数呈指数下降。还介绍了对使用非对齐离散化但通常用于融合建模的两种有限差分方案的方法的简要评估。程序摘要程序名称：Laplace-HDG（拉普拉斯混合不连续伽辽金）CPC 库程序文件链接：http://dx.doi.org/10.17632/c3dhycyvj8.1 许可条款：