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》(Public Law 111-5)资助的。为了克服计算模拟中的各种僵化尺度，该研究团队将开发一个基于无雅可比牛顿-克里洛夫(JFNK)方法的全隐式求解器，该方法带有适用于闪存的预条件，闪存是天体物理界广泛使用的多物理代码框架。Flash提供了块结构的自适应网格细化(AMR)并行模拟网格和基于欧拉流体力学以及N体天体物理的显式求解器。它最初是为模拟Ia型超新星和相关现象而开发的。尽管闪存已经成功地使用其AMR技术解决了一系列允许不同长度比例的问题，但其显式方案对时间紧迫的问题的使用有限。这一弱点的出现是因为显式可压缩解算器在解析刚性系统中不同的时间尺度时效率极低。本项目的主要目标是开发一个基于JFNK的时间精度隐式求解器，并将其与目前Flash中的二阶精度不分裂显式MHD求解器相结合。我们将使用混合(显式/隐式)解算器来执行尖端模拟，以解决太阳日冕问题的加热问题，该问题的非线性物理由僵硬的方程组主导。这一开发将充分利用现有的对Flash代码的专业管理及其广泛的用户基础，以接触到计算物理界。Flash是一个天体物理学社区代码，可以在网上免费获得。

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.