Coupling Solar Simulations with Space Weather: Code...

Coupling Solar Simulations with Space Weather: Code Comparison in SWIFF Consortium

Vyacheslav Olshevsky

1Center for Plasma Astrophysics, Mathematics Department, KU Leuven 2Main Astronomical Observatory, Kyiv, Ukraine [email protected] Co-authors: Anna Lisa Restante1, Giovanni Lapenta1 and Rony Keppens1

mailto:[email protected]

Introduction

20.06.2012 First results of SWIFF 2

SWIFF – Space Weather Integrated Forecasting Framework. The principal goal of SWIFF is development of mathematical models and computational methods to handle multiple physics and multiple scales of space weather.

Multi-physics in space weather


Multi-scale in space weather


Participants


5 scientific and 1 management work packages (WPs):

• WP1. Coordination: Giovanni Lapenta, Katholieke Universiteit Leuven (KU Leuven, Belgium)

• WP2. Multiscale-Multiphysics Modelling: Rony Keppens, Katholieke Universiteit Leuven (KU Leuven, Belgium)

• WP3. Coupling at the Sun: Åke Nordlund, University of Copenhagen (UCPH, Denmark)

• WP4. Coupling in space: Francesco Califano, Università di Pisa (UNIPISA, Italy)

• WP5. Coupling at the Earth: Viviene Pierrard, Belgian Institute for Space Aeronomy (BISA, Belgium)

Numerical Codes


• FlipMHD – viscous resistive MHD code (Brackbill, 1991)

• MPI-AMRVAC – MPI implementation of the Versatile Advection Code with adaptive Mesh Refinement (Keppens et al 2012)

• iPic3D (KU Leuven) • Stagger (UCPH, Denmark) • UNIPI two-fluid code • ASI hybrid PIC code

Benchmarks


• Transition to turbulent reconnection (2D)

• Longcope-Strauss problem (2D)

• Magnetopause challenge (2D)

• CME initiation challenge (3D)

Flux Rope Emergence Setup


𝑩 = 𝜵 ×𝐴 𝑟, 𝜃𝑟 sin𝜃

𝜑� + 𝐵𝜑 𝑟,𝜃 𝜑� ,

A 𝑟,𝜃 = 12𝑞𝑎2𝐵𝑡exp −

𝜔�2 𝑟,𝜃𝑎2

,

𝐵𝜑 𝑟,𝜃 =𝑎𝐵𝑡𝑟 sin𝜃

exp −𝜔�2 𝑟,𝜃𝑎2

.

Semi-circular rope (Fan & Gibson 2004)

Embedded to the background sheared arcade (Aschwanden 2004)

𝐵𝑥 = 𝐵𝑥0 sin 𝑘𝑘 exp −𝑙𝑙 , 𝐵𝑦 = 𝐵𝑦0 sin 𝑘𝑘 exp −𝑙𝑙 , 𝐵𝑧 = 𝐵𝑧0 cos 𝑘𝑘 −𝑙𝑙 ,

𝐵𝑥0 =𝑙𝑘𝐵0,𝐵𝑦0 =

𝛼𝑘𝐵0, 𝑘2 − 𝑙2 − 𝛼2 = 0.

Setup Parameters


𝐵0 = 𝑝0 = 𝜌0 = 1, 𝑢0 = 0, 𝐵𝑡 = 9𝐵0, 𝑅 = 0.375, 𝑞 = −1, 𝑎 = 0.1, 𝐿𝑥 = 1.5, 𝐿𝑦 = 1, 𝐿𝑧 = 1.25, 𝑛𝑥 = 30,𝑛𝑦 = 20,𝑛𝑧 = 25.

Boundary conditions: X – open Y – periodic Top – open Bottom – constant Bz

Results: FlipMHD


Viscous No viscosity

Blue represent magnetic field lines; red contour is at constant density 0.8; The grayscale on the bottom is Bz. Note the destruction of density “tube” in the second case!

FlipMHD vs MPI-AMRVAC


FlipMHD (no viscosity) MPI-AMRVAC

Blue represent magnetic field lines; red contour is at constant density 0.8; The grayscale on the bottom is Bz. In both cases, the tube is destroyed. The behavior of field lines is very similar.

Density Variation in XZ Plane


Results: rise of the rope


Conclusions


The initial configuration leads to immediate emergence of the flux rope, and is handy for comparison of numerical codes The overall behavior is qualitatively the same in FlipMHD and MPI-AMRVAC simulations Rise and rotation of the flux rope is faster in the simulations of MPI-AMRVAC

Future? Particle-in-cell (PIC)


Equations of implicit moment PIC


Equations of motion (moments of Vlasov)

Interpolation of fields to particles

Coupling of fields and particles is nonlinear:

Markidis, Lapenta, Rizwan-uddin (2010), Lapenta (2012)

iPic3D code


• Implicit time-stepping (“implicit moment method”) • Generalized Minimal Residual (GMRes) solver for the coupled

equations of motion – Maxwell system • Divergence cleaning (Conjugate Gradient) – charge density

continuation assurance

Applications • Reconnection on the Sun; magnetosphere; anywhere • Experiments in plasma devices • Ionization of spacecrafts • PIC – hybrid and PIC – fluid coupling • Mass loss in “hot jupiters”?

http://www.swiff.eu


http://www.swiff.eu/

Annex 1. Timeline of the SWIFF project


Coupling Solar Simulations with Space Weather: Code Comparison in SWIFF ConsortiumIntroductionMulti-physics in space weatherMulti-scale in space weatherParticipantsSlide Number 6Numerical CodesBenchmarksFlux Rope Emergence SetupSetup ParametersResults: FlipMHDFlipMHD vs MPI-AMRVACDensity Variation in XZ PlaneResults: rise of the ropeConclusionsFuture? Particle-in-cell (PIC)Equations of implicit moment PICiPic3D codehttp://www.swiff.euAnnex 1. Timeline of the SWIFF project

Coupling Solar Simulations with Space Weather: Code...

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