New techniques for improving the accuracy of gradients for particle and grid simulations of magnetohydrodynamic turbulence.

在天体物理学中，计算磁化气体的流动是理解从恒星形成和演化到黑洞吸积盘等系统的核心。然而，流体建模算法的性能在很大程度上取决于它计算导数或梯度的能力。该项目将实现两种新类型的算法，一种用于粒子，使用多项式回归技术，另一种用于网格，使用高阶，以体积为中心，约束传输，结合调谐有限差分系数。当与去混叠校正一起使用时，这在有限差分代码中产生接近光谱质量，允许以相对较低的成本进行大量并行计算。这些算法将作为独立模块提供，但也可以作为公开分发和广泛使用的代码GADGET2和Pencil的一部分，以促进它们在天体物理学界的广泛使用。这项工作将综合应用数学技术和天体物理模拟。研究成果将被纳入美国自然历史博物馆海登天文馆的太空展览，每年有100万当地游客观看，其中包括10多万纽约市的学童，并每年为数百名教师提供培训。

AST-0612724MaronIn astrophysics, computing the flow of magnetized gases is central to understanding systems ranging from stellar formation and evolution to black hole accretion disks. However, how well a fluid modeling algorithm performs depends greatly on how well it can compute derivatives or gradients. This project will implement two new types of algorithms, one for particles using polynomial regression techniques, and one for grids using high-order, volume-centered, constrained transport, combined with tuned finite difference coefficients. When used with a de-aliasing correction, this yields near spectral quality in a finite difference code, allowing large parallel computations at relatively low cost.These algorithms will be available as independent modules, but also as part of the publicly distributed and broadly used codes GADGET2 and Pencil, in order to promote their wide use in the astrophysical community. The work will integrate applied mathematical techniques and astrophysical simulations. Research results will be incorporated into Space Shows of the Hayden Planetarium at the American Museum of Natural History, viewed locally by a million visitors a year, including over a hundred thousand New York City school children, and into training provided to hundreds of teachers annually.