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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
Rony Keppens & Jannis Teunissen Computational Methods November 2018 2 / 43
Introducing both teachers
1 Introducing both teachers
2 Course Intro & Overview
3 Motivation for numerical astrophysics
4 A prelude: colliding stellar winds
Rony Keppens & Jannis Teunissen Computational Methods November 2018 3 / 43
Introducing both teachers
Nimen Hao!
Rony Keppens & Jannis Teunissen Computational Methods November 2018 4 / 43
Introducing both teachers
Rony Keppens & Jannis Teunissen Computational Methods November 2018 5 / 43
Introducing both teachers
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
Rony Keppens & Jannis Teunissen Computational Methods November 2018 6 / 43
Introducing both teachers
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
Rony Keppens & Jannis Teunissen Computational Methods November 2018 7 / 43
Introducing both teachers
bi li shi de te se: ‘shutiao’: gen helanren you shenme qubie?
Rony Keppens & Jannis Teunissen Computational Methods November 2018 8 / 43
Introducing both teachers
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 !
Rony Keppens & Jannis Teunissen Computational Methods November 2018 9 / 43
Course Intro & Overview
1 Introducing both teachers
2 Course Intro & Overview
3 Motivation for numerical astrophysics
4 A prelude: colliding stellar winds
Rony Keppens & Jannis Teunissen Computational Methods November 2018 10 / 43
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)
Rony Keppens & Jannis Teunissen Computational Methods November 2018 11 / 43
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)
Rony Keppens & Jannis Teunissen Computational Methods November 2018 11 / 43
Course Intro & Overview
Our course in a nutshell: Day 2
• 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 Keppens & Jannis Teunissen Computational Methods November 2018 12 / 43
Course Intro & Overview
Our course in a nutshell: Day 3
• 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
Rony Keppens & Jannis Teunissen Computational Methods November 2018 13 / 43
Course Intro & Overview
Our course in a nutshell: Day 4
• 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
Rony Keppens & Jannis Teunissen Computational Methods November 2018 14 / 43
Course Intro & Overview
Our course in a nutshell: Day 5
• 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
Rony Keppens & Jannis Teunissen Computational Methods November 2018 15 / 43
Course Intro & Overview
Our course in a nutshell: Day 6
• 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
Rony Keppens & Jannis Teunissen Computational Methods November 2018 16 / 43
Motivation for numerical astrophysics
1 Introducing both teachers
2 Course Intro & Overview
3 Motivation for numerical astrophysics
4 A prelude: colliding stellar winds
Rony Keppens & Jannis Teunissen Computational Methods November 2018 17 / 43
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)
Rony Keppens & Jannis Teunissen Computational Methods November 2018 18 / 43
Motivation for numerical astrophysics
• 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
Rony Keppens & Jannis Teunissen Computational Methods November 2018 19 / 43
Motivation for numerical astrophysics
• 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)
Rony Keppens & Jannis Teunissen Computational Methods November 2018 20 / 43
Motivation for numerical astrophysics
• 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)
Rony Keppens & Jannis Teunissen Computational Methods November 2018 21 / 43
Motivation for numerical astrophysics
• 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)
Rony Keppens & Jannis Teunissen Computational Methods November 2018 21 / 43
Motivation for numerical astrophysics
National Supercomputer Centre at Guangzhou hosts Tian-He 2,Fastest supercomputer in the world from 2013 to 2015! (Top500 list)
Rony Keppens & Jannis Teunissen Computational Methods November 2018 22 / 43
Motivation for numerical astrophysics
Rony Keppens & Jannis Teunissen Computational Methods November 2018 23 / 43
Motivation for numerical astrophysics
• 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, . . .
Rony Keppens & Jannis Teunissen Computational Methods November 2018 24 / 43
Motivation for numerical astrophysics
• 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, . . .
Rony Keppens & Jannis Teunissen Computational Methods November 2018 24 / 43
Motivation for numerical astrophysics
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)
Rony Keppens & Jannis Teunissen Computational Methods November 2018 25 / 43
Motivation for numerical astrophysics
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)
Rony Keppens & Jannis Teunissen Computational Methods November 2018 25 / 43
Motivation for numerical astrophysics
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)
Rony Keppens & Jannis Teunissen Computational Methods November 2018 25 / 43
Motivation for numerical astrophysics
Testing - Verification and validation
“Very difficult” : Calder et al. (2002)‘On validating an astrophysical simulation code’http://adsabs.harvard.edu/abs/2002ApJS..143..201C
Rony Keppens & Jannis Teunissen Computational Methods November 2018 26 / 43
Motivation for numerical astrophysics
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/
Rony Keppens & Jannis Teunissen Computational Methods November 2018 26 / 43
A prelude: colliding stellar winds
1 Introducing both teachers
2 Course Intro & Overview
3 Motivation for numerical astrophysics
4 A prelude: colliding stellar winds
Rony Keppens & Jannis Teunissen Computational Methods November 2018 27 / 43
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
Rony Keppens & Jannis Teunissen Computational Methods November 2018 28 / 43
A prelude: colliding stellar winds
• Typical WC parameters: extreme luminosities, M, surface T
Rony Keppens & Jannis Teunissen Computational Methods November 2018 29 / 43
A prelude: colliding stellar winds
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)
Rony Keppens & Jannis Teunissen Computational Methods November 2018 30 / 43
A prelude: colliding stellar winds
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
Rony Keppens & Jannis Teunissen Computational Methods November 2018 31 / 43
A prelude: colliding stellar winds
Monnier et al. 1999; Williams et al. 1995:K-band photometry of WR98a shows period
Rony Keppens & Jannis Teunissen Computational Methods November 2018 32 / 43
A prelude: colliding stellar winds
• 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
Rony Keppens & Jannis Teunissen Computational Methods November 2018 33 / 43
A prelude: colliding stellar winds
• 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)
Rony Keppens & Jannis Teunissen Computational Methods November 2018 34 / 43
A prelude: colliding stellar winds
• 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
Rony Keppens & Jannis Teunissen Computational Methods November 2018 35 / 43
A prelude: colliding stellar winds
Wolf-Rayet binaries:3D mixing zone evolution [θOBθWR isosurface]
Rony Keppens & Jannis Teunissen Computational Methods November 2018 36 / 43
A prelude: colliding stellar winds
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
Rony Keppens & Jannis Teunissen Computational Methods November 2018 37 / 43
A prelude: colliding stellar winds
top view on dust: dragged into OB wake spiral arm
• trailing-leading spiral arm asymmetries⇒ Kelvin-Helmholtz (shear-flow) fine structure on spiral arms
Rony Keppens & Jannis Teunissen Computational Methods November 2018 38 / 43
A prelude: colliding stellar winds
• 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
Rony Keppens & Jannis Teunissen Computational Methods November 2018 39 / 43
A prelude: colliding stellar winds
• 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
Rony Keppens & Jannis Teunissen Computational Methods November 2018 40 / 43
A prelude: colliding stellar winds
• 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 [*]
Rony Keppens & Jannis Teunissen Computational Methods November 2018 41 / 43
A prelude: colliding stellar winds
3D simulations meet 3D printing!
Rony Keppens & Jannis Teunissen Computational Methods November 2018 42 / 43
A prelude: colliding stellar winds
• Any Questions?⇒ Please enjoy the rest of this week with us!
Rony Keppens & Jannis Teunissen Computational Methods November 2018 43 / 43
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