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A Parallel Cut-Cell Algorithm for the Free-Boundary Grad--Shafranov Problem

Liu, Shuang·Tang, Qi·Tang, Xian-zhu
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Abstract

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. Here 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.

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97 MATHEMATICS AND COMPUTINGGrad--Shafranov equationcut-cellfinite differencefree-boundary problem

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Liu, Shuang, Tang, Qi, Tang, Xian-zhu. 2021-12-13. A Parallel Cut-Cell Algorithm for the Free-Boundary Grad--Shafranov Problem. https://doi.org/10.1137/20m1385470

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