An Implicit Solver on Parallel Block-Structured Adaptive Mesh Grid for FLASH

该奖项是根据2009年美国复苏和再投资法案（公法111-5）资助的。为了克服计算模拟中的各种刚性尺度，该研究小组将开发一个基于无雅可比牛顿-克雷洛夫（JFNK）方法的全隐式求解器，并为FLASH提供适当的前置条件，FLASH是天体物理学界广泛使用的多物理场代码框架。FLASH提供了基于欧拉流体力学和n体天体物理学的块结构自适应网格细化（AMR）并行模拟网格和显式求解器。它最初是为模拟Ia型超新星和相关现象而开发的。尽管FLASH已经成功地应用于使用其AMR技术允许不同长度尺度的一系列问题，但其明确的方案对于时间刚性问题的应用有限。这一弱点的出现是因为显式可压缩求解器在求解刚性系统中的不同时间尺度时效率极低。本课题的主要目标是开发一个时间精确的基于jfnk的隐式求解器，并将其与当前FLASH中二阶精确的非分裂显式MHD求解器相结合。我们将使用组合混合（显式/隐式）求解器来执行解决日冕加热问题的尖端模拟，该问题的非线性物理由刚性方程组主导。这一开发将充分利用FLASH代码现有的专业管理及其广泛的用户基础，以达到计算物理社区。FLASH是一个免费的天体物理学社区代码。

This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5).In order to overcome various stiff scales in computational simulations, this research team will develop a fully implicit solver based on a Jacobian-free Newton-Krylov (JFNK) approach with an appropriate preconditioner for FLASH, a multiphysics code framework used widely in the astrophysics community. FLASH provides a block-structured adaptive mesh refinement (AMR) parallel simulation grid and explicit solvers based on Eulerian hydrodynamics as well as N-body astrophysics. It was originally developed for simulations of Type Ia supernovae and related phenomena. Although FLASH has been successfully applied to a range of problems allowing different length scales using its AMR technology, its explicit scheme is of limited use for problems that are stiff in time. This weakness occurs because explicit compressible solvers are extremely inefficient for resolving disparate time scales in the stiff system. The main goal in this project is to develop a time accurate JFNK-based implicit solver and combine it with the current second-order accurate unsplit explicit MHD solver in FLASH. We will use the combined hybrid (explit/implicit) solver to perform cutting-edge simulations addressing the heating of the solar corona problem whose nonlinear physics is dominated by a stiff system of equations. This development will fully leverage the existing professional management of the FLASH code, and its wide user base, to reach the computational physics community. FLASH is an astrophysics community code available online without cost.