AN IMPROVED MULTIPOLE APPROXIMATION FOR SELF-GRAVITY AND ITS IMPORTANCE FOR CORE-COLLAPSE SUPERNOVA SIMULATIONS
AN IMPROVED MULTIPOLE APPROXIMATION FOR SELF-GRAVITY AND ITS IMPORTANCE FOR CORE-COLLAPSE SUPERNOVA SIMULATIONS
复制标题
改进的自重力多极近似及其对核心塌陷超新星模拟的重要性
DOI：
10.1088/0004-637x/778/2/181
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
N. Flocke
中科院分区：
文献类型：
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作者：
S. Couch;C. Graziani;N. Flocke
多极展开的自引力计算是核心坍缩和Ia型超新星等问题的常用方法，其中必须处理单个大质量凝聚。任意坐标系中多极自引力的标准公式有两个重要的误差来源，我们在本文提出的公式中对此进行了修正。误差的第一个来源是由于数值近似有效地将网格单元质量放置在单元的中心点，然后计算该点的引力势，导致多极展开的收敛失败。我们描述了一个新的计划，避免了这个问题，通过计算在细胞表面的引力势。第二个误差来源是由于膨胀中心位置的次优选择，这导致在重力场中高多极l值的角功率，需要高且昂贵的多极截止值lmax。通过在引力场中引入角幂的全局度量，我们证明了展开的最佳坐标是平方密度加权平均位置。我们提出了新的多极自引力算法，在FLASH模拟框架中实现，两个严格的测试问题：MacLaurin球体的精确解析解是已知的，核心塌陷超新星。我们表明，核心塌陷模拟，特别是冲击膨胀，原中子星星运动和动量守恒的关键可观的，是非常敏感的多极引力的准确性，其计算的准确性大大提高了我们重新制定的求解器。
Self-gravity computation by multipole expansion is a common approach in problems such as core-collapse and Type Ia supernovae, where single large condensations of mass must be treated. The standard formulation of multipole self-gravity in arbitrary coordinate systems suffers from two significant sources of error, which we correct in the formulation presented in this article. The first source of error is due to the numerical approximation that effectively places grid cell mass at the central point of the cell, then computes the gravitational potential at that point, resulting in a convergence failure of the multipole expansion. We describe a new scheme that avoids this problem by computing gravitational potential at cell faces. The second source of error is due to sub-optimal choice of location for the expansion center, which results in angular power at high multipole l values in the gravitational field, requiring a high—and expensive—value of multipole cutoff lmax. By introducing a global measure of angular power in the gravitational field, we show that the optimal coordinate for the expansion is the square-density-weighted mean location. We subject our new multipole self-gravity algorithm, implemented in the FLASH simulation framework, to two rigorous test problems: MacLaurin spheroids for which exact analytic solutions are known, and core-collapse supernovae. We show that key observables of the core-collapse simulations, particularly shock expansion, proto-neutron star motion, and momentum conservation, are extremely sensitive to the accuracy of the multipole gravity, and the accuracy of their computation is greatly improved by our reformulated solver.