Adaptive Hybridizable Discontinuous Galerkin discretization of the Grad-Shafranov equation by extension from polygonal subdomains
Adaptive Hybridizable Discontinuous Galerkin discretization of the Grad-Shafranov equation by extension from polygonal subdomains
复制标题
通过多边形子域扩展的 Grad-Shafranov 方程的自适应可杂化不连续伽辽金离散化
DOI：
10.1016/j.cpc.2020.107239
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发表时间：
2019
期刊：
影响因子：
--
通讯作者：
A. Cerfon
中科院分区：
文献类型：
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作者：
Tonatiuh S'anchez;Manuel E. Solano;A. Cerfon
针对轴对称约束装置中磁等离子体平衡的半线性椭圆边值问题，提出了一种高阶自适应数值求解器。在固定边界的情况下，该方程是在弯曲的域与分段光滑的弯曲边界，可能会出现角。我们提出的解决方案的方法是基于杂交不连续Galerkin方法和回避几何形状一致的三角剖分由于转移技术，允许近似的解决方案，只使用一个多边形子集作为计算域的需要。此外，求解器具有自动网格细化驱动的残差为基础的后验误差估计。当网格局部细化时，计算域自动更新，以便始终保持实际边界和计算边界之间的距离为局部网格直径的量级。数值证据的适用性的估计作为一个近似的误差测量物理相关的平衡与压力pneumalals，内部运输障碍，和当前的孔在现实的几何形状。
We propose a high-order adaptive numerical solver for the semilinear elliptic boundary value problem modeling magnetic plasma equilibrium in axisymmetric confinement devices. In the fixed boundary case, the equation is posed on curved domains with piecewise smooth curved boundaries that may present corners. The solution method we present is based on the hybridizable discontinuous Galerkin method and sidesteps the need for geometry-conforming triangulations thanks to a transfer technique that allows to approximate the solution using only a polygonal subset as computational domain. Moreover, the solver features automatic mesh refinement driven by a residual-based a posteriori error estimator. As the mesh is locally refined, the computational domain is automatically updated in order to always maintain the distance between the actual boundary and the computational boundary of the order of the local mesh diameter. Numerical evidence is presented of the suitability of the estimator as an approximate error measure for physically relevant equilibria with pressure pedestals, internal transport barriers, and current holes on realistic geometries.