computational methods for astrophysical applicationsu0016541/mhd_sheets_pdf/... · 2019-01-21 · 4...

Computational Methods for AstrophysicalApplications

Rony Keppens & Jannis Teunissen

Centre for mathematical Plasma Astrophysics (CmPA), KU Leuven, BelgiumCentre for Mathematics and Informatics (CWI), Amsterdam, The Netherlands

Rony Keppens & Jannis Teunissen Computational Methods November 2018 1 / 43

Lesson 1A: Course intro & overview


Introducing both teachers

1 Introducing both teachers

2 Course Intro & Overview

3 Motivation for numerical astrophysics

4 A prelude: colliding stellar winds



Nimen Hao!



Jannis Teunissen

• Homepage (http://www.teunissen.net)⇒ Master Computational Science, University of Amsterdam⇒ PhD in Computational Plasma Physics at CWI (2015)⇒ Postdoc at CmPA, KU Leuven, since July 2016⇒ Tenure-track at CWI, Multiscale Dynamics: October 2018


http://www.teunissen.net


Rony Keppens

• (http://perswww.kuleuven.be/Rony_Keppens)⇒ Mathematics at KU Leuven, Belgium⇒ PhD at High Altitude Observatory, NCAR Boulder & KU

Leuven (1995): studying p-mode interactions with sunspots⇒ Postdoc at Kiepenheuer Institute for Solar Physics & at

FOM-Institute for Plasma Physics, The Netherlands⇒ Scientific Project Leader for Numerical Plasma Dynamics⇒ Previous affiliations with: Utrecht University,

Observatoire de Paris, Nanjing University• Full professor and Division Chair at CmPA, KU Leuven


http://perswww.kuleuven.be/Rony_Keppens


bi li shi de te se: ‘shutiao’: gen helanren you shenme qubie?



Nimen she shei?

• women xihuan gen nimen liaotian yi xia, wei shenme nimencanjia women de ke ...

⇒ women ye baoqian: bixu yong yingwen liao yi liao, yinweiwomen de hanyu bijiao cha !


Course Intro & Overview







Our course in a nutshell: Day 1

1 Day 1: Goals & program2 Motivation & context for

numerical simulations3 A prelude: simulating

colliding stellar winds

— truncation versus rounding errors

— ODEs & Finite Difference methods

— Runge-Kutta methods, stability,implicit methods— HANDS-ON solving ODEs

• installing and using MPI-AMRVAC (see http://amrvac.org)


http://amrvac.org



• Jannis: PDE types, numerical solution methods⇒ focus towards (scalar linear) hyperbolic PDEs

• Rony: Continue with scalar linear hyperbolic PDEs⇒ from single scalar to multiple linear hyperbolic PDEs

• HANDS-ON advect yourself with MPI-AMRVAC




• Rony: nonlinear (hyperbolic) PDEs⇒ single nonlinear hyperbolic PDE (Burger’s equation)⇒ beyond inviscid Burger’s equation (advection-diffusion

versus advection-dispersion)⇒ systems of nonlinear hyperbolic PDEs: isothermal hydro

• Jannis: FD, FV, FE solution strategy basics⇒ implicit advection treatments

• HANDS-ON solving nonlinear PDEs numerically




• Jannis: parabolic and elliptic PDEs⇒ applications and solution strategies

• Rony: The (hyperbolic) Euler equations of gas dynamics⇒ shocks and discontinuities, Riemann problem⇒ shock-capturing aspects, TVDLF scheme

• HANDS-ON heat equation/diffusion, Riemann problem for Euler




• Jannis: tips for writing your own solvers, validation & verification• Rony: gas dynamics continued

⇒ shocks in compressible hydro, instabilities(Kelvin-Helmholtz, Rayleigh-Taylor), advanced hydrodynamicapplications in (astro)physics• HANDS-ON hydro simulations with MPI-AMRVAC




• Jannis: Electric discharges and fluid versus particle basedmethods for discharges• Rony: Magnetohydrodynamics and particle acceleration• HANDS-ON basic Particle-In-Cell simulations, charged particle

motion in EM fields


Motivation for numerical astrophysics







Why

• Astrophysical research invariably involves numericsTheoretical astrophysics ≈ computationally aided researchhttp://iopscience.iop.org/journal/0004-637X ApJhttp://mnras.oxfordjournals.org/ MNRAShttp://www.aanda.org/index.php A&A

• Trends to create virtual observatories, with a significantcode-based component, e.g. http://www.ivoa.net/grouped in International Virtual Observatory Alliance• numerical simulations used to interpret, analyse or predict

observations. Centres established, e.g.⇒ http://csem.engin.umich.edu/

Space weather: Centre for Space Environment Modeling (CSEM)


http://iopscience.iop.org/journal/0004-637X

http://mnras.oxfordjournals.org/

http://www.aanda.org/index.php

http://www.ivoa.net/

http://csem.engin.umich.edu/


• Compute impact Coronal Mass Ejection on Earth’smagnetosphere faster than real time

⇒ challenge (few days), range of scales– BATS-R-US code (block-adaptive tree solver Roe upwind

scheme) from Space Weather Modeling Framework– Gombosi, Tóth et al., Univ. of Michigan:

Centre for Space Environment movie



• However, large differences in approach/needs. Search engines,data mining in huge archives, real-time data processing→ trendto use GRID technology. Not treated here.

Focus: efforts to use modern high performance codes inidealized or ‘realistic’ applications, motivated by astrophysics

Most info we receive from the sky is as electromagnetic radiation,static/dynamic models produced by software should be processedto synthetic observations (using known satellite/telescopesensitivity & plasma physics insights to yield images)



• techniques vary, recurring themes:⇒ borrow, improve and develop new algorithms in use for

Computational Fluid Dynamics. These model air flows aboutcomplete airplanes, trains, cars, . . .(example from COOLFluiD at Von Karman Institute)

⇒ exploit power of parallel computing (requiring codingefforts as memory/data is distributed over differentprocessors/CPUs: need to communicate data across networks),e.g. with MPI (Kunming course: Xia Chun)



National Supercomputer Centre at Guangzhou hosts Tian-He 2,Fastest supercomputer in the world from 2013 to 2015! (Top500 list)



• competitive research: internationally peer-reviewed calls⇒ PRACE: Partnership for Advanced Computing in Europe

http://www.prace-ri.eu/

⇒ US Department of Energy: Advanced ScientificComputing Research http://science.energy.gov/ascr/

• many laboratory or astrophysics (plasma) applications!⇒ combustion & ignition, turbulence, supernovae explosions,

numerical relativity, circumstellar nebulae⇒ state-of-the-art: 3D simulations, wide range of length and

timescales, integrate (magneto)hydrodynamics with complexnuclear physics, chemistry, radiative losses, . . .


http://www.prace-ri.eu/

http://science.energy.gov/ascr/


Coding - Specific for Astrophysics

1 many general codes available(MPI-AMRVAC , ATHENA, FLASH, PLUTO, RAMSES,. . .)

verify source code access (open source versus binary executables)sometimes code only needs minor modifications⇒ but is difficult to get, understand, modify

2 Define geometry, initial and boundary conditions and resolutionneeds of the computational approach

Cartesian versus cylindrical grid, adaptive mesh refinement, . . .Discontinuities: shock capturing methods, turbulence: spectraldefine minimum spatial resolution, identify all timescales involved

3 Try to work dimensionless (SI versus cgs units cause of muchconfusion!): reformulate to order unity input/output ranges

4 Math on computers:avoid divisions, consider optimal ordering of arrays and loopscheck for positive arguments in

√x , ln , etc.

think about precision of floating point numbers (use double)



Testing - Verification and validation

“Very difficult” : Calder et al. (2002)‘On validating an astrophysical simulation code’http://adsabs.harvard.edu/abs/2002ApJS..143..201C


http://adsabs.harvard.edu/abs/2002ApJS..143..201C


Testing - Verification and validation

“Very difficult” : Calder et al. (2002)‘On validating an astrophysical simulation code’http://adsabs.harvard.edu/abs/2002ApJS..143..201C

Verification & Validationverify: solve the equations rightvalidate: solve the right equationsdevise experiment to compare: lab/simulation confrontationsvalidation tests for fluid instabilities: Rayleigh-Taylor anecdote

⇒ must consider error in experiment/measurementstate-of-the-art modeling: Type Ia supernovae and labexperiments: see http://flash.uchicago.edu/


http://adsabs.harvard.edu/abs/2002ApJS..143..201C

http://flash.uchicago.edu/

A prelude: colliding stellar winds







Wolf-Rayet stages for massive O stars

• Wolf-Rayet stars (Charles Wolf/Georges Rayet 1867)⇒ unusually broad emission lines⇒ WN subtype of strong He and Nitrogen⇒ WC subtype with He and Carbon, Oxygen

• Massey 2003 (+Conti 1976): stages of massive O star evolution⇒ M reveals CNO cycle [WN], then He-burn [WC] at surface



• Typical WC parameters: extreme luminosities, M, surface T



Modern views: direct imaging of dust shells

• cfr. Nature 398, 487, 1999: binarity: clue for dust form/survivein WR circumstellar environment! 2008 ApJ Tuthill et al• Cartoon view: dust can form in WCR (Tuthill et al. 1999)



WR 98a: WC9 + OB binary

• observations at 2.2 µm [Monnier et al, 1999]

⇒ second ‘pinwheel nebula’ discovered, archimedian spiralgives Porb ≈ 1.55 yr or separation of a = 4AU

⇒ Tuthill webpage WR98a views



Monnier et al. 1999; Williams et al. 1995:K-band photometry of WR98a shows period



• wind-wind interactions depend on momentum flux ratio of winds

η ≡ MOBvOB

MWRvWR≈ 0.022 (WR98a)

⇒ WR dominates, supersonic (900 km/s, Mach 76 [WR])• Hendrix et al. 2016, MNRAS: 3D model for WR 98a to 1300 AU

⇒ Wind collision region: details to 1 % of a ∼ 4AU⇒ HD+dust: dynamic dust formation & redistribution⇒ synthetic infrared observations (Keck, ALMA, E-ELT)⇒ follow multiple periods & virtual photometry

• MPI-AMRVAC for HD+dust, SKIRT for synthetic views



• solve coupled gas-dust equations (adiabatic)

∂ρ

∂t+∇ · (ρv) = Sint

ρ,WR−OB − Smixρ

∂(ρv)∂t

+∇ · (ρvv) +∇p = fd + Sintρv,WR−OB − Smix

ρv

∂e∂t

+∇ · [(p + e)v] = v · fd + Sinte,WR−OB − Smix

e

∂ρd

∂t+ ∇ · (ρdvd) = Smix

ρd

∂(ρdvd)

∂t+ ∇ · (ρdvdvd) = −fd + Smix

ρd vd

⇒ Epstein drag

fd = (1− α(T ))

√8γpπρ

ρρd

ρpad(vd − v)



• domain of size 320a× 320a× 140a⇒ 11 AMR levels, effective 81920× 81920× 24576⇒ internal boundaries for wind zones on Keplerian orbit⇒ tracers for identifying mixing zone between both winds

∂θWR

∂t+ v · ∇θWR = Sint

θWR

∂θOR

∂t+ v · ∇θOR = Sint

θOR

⇒ mixing used in heuristic model for dust insertion/creation



Wolf-Rayet binaries:3D mixing zone evolution [θOBθWR isosurface]



subgrid dust formation [local rate φ, geometric Din = 20 andDout = 213 AU]: gas to dust in (dynamically relocating) mixing layer

• values from observations (0.2% gas-to-dust, dust shell sizes)⇒ dust forms in high density regions with wind-wind mixing



top view on dust: dragged into OB wake spiral arm

• trailing-leading spiral arm asymmetries⇒ Kelvin-Helmholtz (shear-flow) fine structure on spiral arms



• MPI-AMRVAC couples to Monte Carlo SKIRT code (UGent)

⇒ time evolution of gas and dust on block-AMR grid• SKIRT: can read in native ∗.dat format files from MPI-AMRVAC

⇒ Monte Carlo treats scattering/absorption/re-emission ondust, outputs: virtual (infrared) observations, convolved withinstrument specifics



• object at 1900 pc• Keck [50 mas, 2.45 µm] or ALMA [6 mas, 400 µm] resolutions

(virtual views with SKIRT postprocessing of dust distribution) [20vs 2 pixel convolutions]

⇒ WR98a@Keck [2.4µm] vs WR98a@ALMA [400µm]⇒ KH substructure visible by ALMA, smeared by Keck⇒ leading/trailing arm asymmetries predicted



• Virtual photometry: effect of orientation (face-on to edge-on)⇒ use 25 pixel radius on images to sum all flux values⇒ variation consistent with inferred 35◦ angle orientation [*]



3D simulations meet 3D printing!



• Any Questions?⇒ Please enjoy the rest of this week with us!


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