|An Implicit Solver on A Parallel Block-Structured Adaptive Mesh Grid for FLASH
|459, 6th International Conference of Numerical Modeling of Space Plasma Flows (ASTRONUM 2011)
|Lee, D.; Gopal, S.; Mohapatra, P.
|We introduce a fully implicit solver for FLASH based
on a Jacobian-Free Newton–Krylov (JFNK) approach with
an appropriate preconditioner.
The main goal of developing this JFNK-type implicit solver is to provide efficient high-order
numerical algorithms and methodology for simulating stiff systems of
differential equations on large-scale parallel computer architectures.
A large number of natural problems in nonlinear
physics involve a wide range of spatial and time scales of interest.
A system that encompasses such a wide magnitude of scales is described as “stiff.”
A stiff system can arise in many different fields of physics, including
fluid dynamics/aerodynamics, laboratory/space plasma physics, low Mach
number flows, reactive flows, radiation hydrodynamics, and geophysical
flows. One of the big challenges in solving such a stiff system using current-day
computational resources lies in resolving
time and length scales varying by several orders of magnitude.
We introduce FLASH's preliminary implementation of a time-accurate
JFNK-based implicit solver in the framework of FLASH's unsplit hydro solver.