# Presentation: 153662

## Center for Magnetic Reconnection Studies: Present Status, Future Plans

- Amitava Bhattacharjee
*The University of Iowa*
- PSACI/SciDAC Meeting
- Princeton, June 3-4, 2002

## University of Iowa: A. Bhattacharjee (PI and Director), B. Chandran, N. Bessho, L.-J. Chen, K. Germaschewski, Z. W. Ma, J. Maron, C. S. Ng, P. Zhu

University of Chicago: R. Rosner (PI), F. Cattaneo, A. Dubey, T. Linde, A. Siegel

University of Texas at Austin: R. Fitzpatrick (PI), F. Waelbroeck, P. Watson

*University of Chicago*: R. Rosner (PI), F. Cattaneo, A. Dubey, T. Linde, A. Siegel
*University of Texas at Austin*: R. Fitzpatrick (PI), F. Waelbroeck, P. Watson

- Center for Magnetic Reconnection Studies*University of Iowa-University of Chicago-University of Texas at Austin*Interdisciplinary group drawn from applied mathematics, astrophysics, computer science, fluid dynamics, plasma physics, and space science communities

## Outline

- Principal objectives: Magnetic Reconnection Code (MRC), its attributes, and applications
*Flash *framework
- Adaptive Mesh Refinement (AMR) basics
- 2D Hall MHD: applications to sawtooth physics and scaling studies
- Spherical tearing mode: new theoretical paradigm for 3D reconnection
- Collaboration with the ISIC groups
- Outreach

## Principal Objectives

- <date/time>

- Magnetic Reconnection Code (MRC)

-  A fully 3D code which integrates the equations of Hall MHD
-  Geometry: slab (2002), cylindrical and toroidal (2003)
-  Flexible boundary conditions: free as well as forced reconnection studies
-  Options for equations of state
-  Modular code, with the flexibility to change algorithms if necessary
-  Massively parallel with Adaptive Mesh Refinement
-  Code must perform and scale well, be highly portable, and be easy to maintain, modify and evolve into the future
-   Framework defined by FLASH---developed by active collaboration with computer scientists

## Applications to Astrophysical, Fusion/Laboratory and Space Plasmas

- <date/time>

- Sawtooth oscillations in tokamaks, magnetotail substorms, and solar flares
-   Error-field studies in toroidal plasmas (*Richard Fitzpatrick, next presentation*)
-  Astrophysical and reversed-field pinch  dynamo studies
-  Simulation of laboratory magnetic reconnection experiments (e.g., MRX at Princeton, VTF at MIT)

## Flash in a nutshell

- <date/time>

*Flash* is:
- Modular, uses PARAMESH for AMR, MPI, and HDF5 (parallel I/O)
- Selected features:
- Solves compressible multi-fluid hydro/resistive MHD
- Broad range of equations of state
- Energy transport: thermal conduction; radiative transport
- Emphasis has been on:
- Portability - just needs MPI, F90 & C compilers, Python interpreter optional
- Flexibility/documentation - easy to add modules and set up new problems, available in the public domain (via web)
- Performance - optimized for general distributed memory cache-based machines

- _[http://flash.](http://flash.uchicago.edu/)__[uchicago](http://flash.uchicago.edu/)__[.](http://flash.uchicago.edu/)__[edu](http://flash.uchicago.edu/)_

*Flash* in a nutshell

## Flash hydro/MHD applications 

*Cellular detonation*

*Compressed turbulence*

*Helium burning on neutron stars*

*Richtmyer-Meshkov instability*

*Laser-driven shock instabilities*

*Nova outbursts on white dwarfs*

*Rayleigh-Taylor instability*

*Flame-vortex interactions*

*Wave breaking on white dwarfs*

*Shortly: Relativistic accretion onto NS*

*Orzag/Tang MHD*
*vortex*

*Type Ia Supernova*

*Intracluster interactions*

*Magnetic*
*Rayleigh-Taylor*

## Scaling on a model reconnection problem

## AMR basics

-  Effective methods work on regular grids
-  Cover integration with coarse grid
-  Add new levels with finer grid spacing as necessary
-  Sub stepping in time

## AMR basics

- Grid generation:
-  Periodically check all grid points whether we run out of resolution
-  Cover these points efficiently with new grids

- Numerical methods:
-  Application of well known finite difference techniques possible
-  Unavoidable small mismatches at boundaries between levels of  different resolutions can   be handled using shock capturing schemes (we used a third-order semi discrete scheme,   Kurganov/Levy (2000) with a compact 4th order poisson solver, E/Liu (2000))

- Parallelization:
-  Distribute grids onto processors

## AMR basics

- _Example: 2D MHD (previous work)_

- Efficiency of AMR

- High effective resolution

- Level	# grids	# grid points
- 0	1	70225
- 1	83	146080
- 2	103	268666
- 3	153	545316
- 4	197	1042132
- 5	404	1926465
- 6	600	1967234

- Grid points in adaptive simulation:	6976118
- Grid points in non-adaptive simulation:	268730449
- Ratio	0.02

**log**

## 2D Hall MHD: m=1 sawtooth instability

- Model equations:

- (Ottaviani/Porcelli 1993)
- (Grasso/Pegoraro/Porcelli/Califano 1999)

## 2D Hall MHD, s = 0

- vorticity

- F

- magnetic
- stream function

- t = 300

- t = 455

- t = 430

- vorticity

- t = 465

- t = 462

- t = 460

- zoom, t = 462

## 2D Hall MHD, s = 0.4

- Coverage with adaptive grids

- Evolution of island width

- de= 0.1

- de= 0.4

## Remarks

- Implementation of AMR in Hall MHD enables possibility of unprecedented resolution of current and vorticity layers
- Dynamics shows linear and nonlinear exponential growth, followed by a near-explosive late nonlinear phase
- Dynamics of island width evolution with time appears to be robust with respect to the level of AMR resolution, even though higher levels of resolution clearly uncover new secondary dynamics and structures, not reported in earlier studies
- Scaling studies currently under way

## Scaling of quasi-steady reconnection

- (Phys. Rev. Lett. 87, 265003, 2001)

- Analytical model

## The Spherical Tearing Mode

- (with John Greene, *General Atomics*)

## Slide 18

## TOPS (Terascale Optimal PDE Simulations): David Keyes and Florin Dobrian 
Newton-Krylov-Schwarz (NKS) implicit algorithms for system of PDEs (Hall MHD) 
PETSc (Portable Extensible Toolkit for Scientific Computing) implementation of NKS                     
APDEC (An Algorithmic and Software Framework for Applied PDEs): Phillip Colella
Adaptive Mesh Refinement for 3D Hall MHD

- <date/time>

- TOPS (Terascale Optimal PDE Simulations): David Keyes and Florin Dobrian
- Newton-Krylov-Schwarz (NKS) implicit algorithms for system of PDEs (Hall MHD)
- PETSc (Portable Extensible Toolkit for Scientific Computing) implementation of NKS
- APDEC (An Algorithmic and Software Framework for Applied PDEs): Phillip Colella
- Adaptive Mesh Refinement for 3D Hall MHD

- Collaboration with ISIC groups: TOPS and APDEC

## Roadmap for collaboration

- TOPS: put implicit time stepping into 2D Cartesian PDE thermally driven cavity example with multiple coupled components
- CMRS: cast model 2D Hall MHD problem in PETSc format, to have access to multiple solution methods, including multigrid
- TOPS & CMRS: identify the numerical complexity benefits from implicitness (in suppressing fast timescales) and quantify (semi-implicit versus fully implicit)
- TOPS & CMRS: generalize model Hall MHD physics
- CMRS: code to explore large-scale parallelism opportunities in 3D Cartesian context
- TOPS, APDEC, CMRS: incorporate AMR

## Outreach  

- Mini-Workshop for Basic Studies in Fusion Science, DPP-APS, Long Beach, October 2001 (organized by CMRS and LAPD group, UCLA)
- Magnetofluid Modeling Workshop, August, 2002 (organized by F. Waelbroeck and other members of the CMRS, CEMM groups)
-  Mini-Conference on “Singularity formation in plasmas and fluids”, DPP-APS, Orlando, November 2002 (organized by CMRS)
- Extended Workshop on Magnetic Reconnection at Aspen Center for Physics, summer 2003 (organized by CMRS)