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

为了克服计算模拟中的各种僵硬尺度，该研究小组将开发一个基于Jacobian自由牛顿-克雷洛夫（JFNK）方法的全隐式求解器，并为FLASH（一种广泛用于天体物理学界的多物理场代码框架）提供适当的预处理器。 FLASH提供了一个块结构的自适应网格细化（AMR）并行模拟网格和显式求解器的基础上欧拉流体动力学以及N体天体物理学。它最初是为模拟Ia型超新星和相关现象而开发的。虽然FLASH已经成功地应用于一系列问题，允许不同的长度尺度使用其AMR技术，其明确的计划是有限的使用时间是僵硬的问题。出现这种弱点是因为显式可压缩求解器在解决刚性系统中的不同时间尺度时效率极低。本计画的主要目标是发展一个时间精确的基于JFNK的隐式求解器，并将其与目前FLASH中的二阶精确的不分裂显式MHD求解器联合收割机结合。我们将使用组合的混合（显式/隐式）求解器来执行尖端的模拟，解决太阳日冕问题的加热，其非线性物理主要是由一个僵硬的方程组。 这项开发将充分利用现有的专业管理的FLASH代码，其广泛的用户群，达到计算物理界。 FLASH是一个天体物理学社区代码，可以免费在线使用。

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.