A Hybridizable Discontinuous Galerkin solver for the Grad-Shafranov equation
A Hybridizable Discontinuous Galerkin solver for the Grad-Shafranov equation
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Grad-Shafranov方程的可混合间断伽辽金求解器
DOI：
10.1016/j.cpc.2018.09.013
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
Manuel E. Solano
中科院分区：
文献类型：
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作者：
Tonatiuh Sánchez;Manuel E. Solano
在轴对称聚变反应堆中，平衡磁构型可以用半线性椭圆方程（即Grad-Shafranov方程）的解来表示，该方程的解决定了磁场的极向分量。当约束区域的几何形状已知时，问题就变成了一个内狄利克雷边值问题。提出了一种基于杂交不连续伽辽金法的高阶求解器。所得算法(1)为通量函数及其梯度提供了高阶收敛性；(2)通过多边形网格的扩展引入了一种处理分段光滑几何的新方法；(3)可以处理具有非光滑边界和x点的几何；(4)通过加速的两网格不动点迭代处理半线性。通过计算验证了算法的有效性，在与实际设备（具有单零和双零分流器的ITER， NSTX， ASDEX升级和场反转配置）相似的配置下已知解析解的情况下，验证了算法的有效性。
In axisymmetric fusion reactors, the equilibrium magnetic configuration can be expressed in terms of the solution to a semi-linear elliptic equation known as the Grad–Shafranov equation, the solution of which determines the poloidal component of the magnetic field. When the geometry of the confinement region is known, the problem becomes an interior Dirichlet boundary value problem. We propose a high order solver based on the Hybridizable Discontinuous Galerkin method. The resulting algorithm (1) provides high order of convergence for the flux function and its gradient, (2) incorporates a novel method for handling piecewise smooth geometries by extension from polygonal meshes, (3) can handle geometries with non-smooth boundaries and x-points, and (4) deals with the semi-linearity through an accelerated two-grid fixed-point iteration. The effectiveness of the algorithm is verified with computations for cases where analytic solutions are known on configurations similar to those of actual devices (ITER with single null and double null divertor, NSTX, ASDEX upgrade, and Field Reversed Configurations).