A parallel cut-cell algorithm is described to solve the free-boundary problem of the Grad-Shafranov equation. The algorithm reformulates the free-boundary problem in an irregular bounded domain and its important aspects include a searching algorithm for the magnetic axis and separatrix, a surface integral along the irregular boundary to determine the boundary values, an approach to optimize the coil current based on a targeting plasma shape, Picard iterations with Aitken's acceleration for the resulting nonlinear problem, and a Cartesian grid embedded boundary method to handle the complex geometry. The algorithm is implemented in parallel using a standard domain-decomposition approach and a good parallel scaling is observed. Numerical results verify the accuracy and efficiency of the free-boundary Grad-Shafranov solver.
翻译:描述平行切分细胞算法是为了解决Grad-Shafranov等式的自由边界问题。算法重塑了非常规封闭域的自由边界问题,其重要方面包括:磁轴和分离轴的搜索算法,这是沿非常规边界确定边界值的一个整体表面,一种基于目标等离子形状优化卷流的方法,Aitken加速处理由此产生的非线性问题的Picard迭代法,以及一种处理复杂几何学的Cartesian网格嵌入边界方法。算法同时使用标准的域分解法和良好的平行缩放法执行。数字结果验证了自由边界Grad-Shafranov求解器的准确性和有效性。