Methods, Languages and Tools for Future System Development

Steffen, Bernhard

doi:10.1007/978-3-319-91908-9_14

Cited by 6 publications

(8 citation statements)

References 31 publications

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“…The analytical solutions of the cooled spectrum in equation (35) and of the self-similar spectrum in equation (36) need a functional representation of the spectrum at time t 0 for the entire momentum range. As the spectrum is calculated on a discrete momentum grid with piecewise constant values, we calculate an interpolation function at every time with the Steffen's method (Steffen 1990), which is cubic and monotonic between neighbouring discrete momenta. This interpolation function is used to calculate the analytic solution after a time step ∆t.…”

Section: General Solutionsmentioning

confidence: 99%

Evolution of cosmic ray electron spectra in magnetohydrodynamical simulations

Winner

Pfrommer

Girichidis

et al. 2019

Monthly Notices of the Royal Astronomical Society

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Cosmic ray (CR) electrons reveal key insights into the non-thermal physics of the interstellar medium (ISM), galaxies, galaxy clusters, and active galactic nuclei by means of their inverse Compton γ-ray emission and synchrotron emission in magnetic fields. While magnetohydrodynamical (MHD) simulations with CR protons capture their dynamical impact on these systems, only few computational studies include CR electron physics because of the short cooling time-scales and complex hysteresis effects, which require a numerically expensive, high-resolution spectral treatment. Since CR electrons produce important non-thermal observational signatures, such a spectral CR electron treatment is important to link MHD simulations to observations. We present an efficient post-processing code for Cosmic Ray Electron Spectra that are evolved in Time (crest) on Lagrangian tracer particles. The CR electron spectra are very accurately evolved on comparably large MHD time steps owing to an innovative hybrid numerical-analytical scheme. crest is coupled to the cosmological MHD code arepo and treats all important aspects of spectral CR electron evolution such as adiabatic expansion and compression, Coulomb losses, radiative losses in form of inverse Compton, bremsstrahlung and synchrotron processes, diffusive shock acceleration and reacceleration, Fermi-II reacceleration, and secondary electron injection. After showing various code validations of idealized one-zone simulations, we study the coupling of crest to MHD simulations. We demonstrate that the CR electron spectra are efficiently and accurately evolved in shock-tube and Sedov-Taylor blast wave simulations. This opens up the possibility to produce self-consistent synthetic observables of non-thermal emission processes in various astrophysical environments.

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Section: General Solutionsmentioning

confidence: 99%

Evolution of cosmic ray electron spectra in magnetohydrodynamical simulations

Winner

Pfrommer

Girichidis

et al. 2019

Monthly Notices of the Royal Astronomical Society

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“…In fact, it requires matrix-by-matrix multiplications and, in particular, the calculation of second-order accurate numerical derivatives appears to be the most expensive part of the method. Moreover, Ibgui et al (2013) explained that the calculation of numerical derivatives proposed by Steffen (1990) is sensibly slower than the one proposed by Fritsch & Butland (1984). However, the derivatives provided by Fritsch & Butland (1984) are second-order accurate on uniform grids only and they drop to first-order accuracy on non-uniform grids (see Janett & Paganini 2018).…”

Section: Cubic Hermitian Methodsmentioning

confidence: 99%

“…However, the derivatives provided by Fritsch & Butland (1984) are second-order accurate on uniform grids only and they drop to first-order accuracy on non-uniform grids (see Janett & Paganini 2018). For this reason, the version by Steffen (1990) is used here.…”

Section: Cubic Hermitian Methodsmentioning

confidence: 99%

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Formal Solutions for Polarized Radiative Transfer. IV. Numerical Performances in Practical Problems

Janett

Steiner

Belluzzi

2018

ApJ

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The numerical computation of reliable and accurate Stokes profiles is of great relevance in solar physics. In the synthesis process, many actors play a relevant role: among them the formal solver, the discrete atmospheric model, and the spectral line. This paper tests the performances of different numerical schemes in the synthesis of polarized spectra for different spectral lines and atmospheric models. The hierarchy between formal solvers is enforced, stressing the peculiarities of high-order and low-order formal solvers. The density of grid points necessary for reaching a given accuracy requirement is quantitatively described for specific situations.

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“…Fritsch & Carlson (1980) proposed a two-pass algorithm to recover such derivatives. Later on, Fritsch & Butland (1984) and Steffen (1990) added alternative formulas to recover secondorder accurate first derivatives 7 . Auer (2003) suggested the use of monotonic Hermite interpolants in radiative transfer problems and Ibgui et al (2013) used monotonic cubic Hermite polynomials (version of Fritsch & Butland 1984) in the IRIS code.…”

Section: Cubic Hermite Splinesmentioning

confidence: 99%

Discontinuities in numerical radiative transfer

Janett

2019

A&A

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Observations and magnetohydrodynamic simulations of solar and stellar atmospheres reveal an intermittent behavior or steep gradients in physical parameters, such as magnetic field, temperature, and bulk velocities. The numerical solution of the stationary radiative transfer equation is particularly challenging in such situations, because standard numerical methods may perform very inefficiently in the absence of local smoothness. However, a rigorous investigation of the numerical treatment of the radiative transfer equation in discontinuous media is still lacking. The aim of this work is to expose the limitations of standard convergence analyses for this problem and to identify the relevant issues. Moreover, specific numerical tests are performed. These show that discontinuities in the atmospheric physical parameters effectively induce first-order discontinuities in the radiative transfer equation, reducing the accuracy of the solution and thwarting high-order convergence. In addition, a survey of the existing numerical schemes for discontinuous ordinary differential systems and interpolation techniques for discontinuous discrete data is given, evaluating their applicability to the radiative transfer problem.

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Methods, Languages and Tools for Future System Development

Cited by 6 publications

References 31 publications

Evolution of cosmic ray electron spectra in magnetohydrodynamical simulations

Evolution of cosmic ray electron spectra in magnetohydrodynamical simulations

Formal Solutions for Polarized Radiative Transfer. IV. Numerical Performances in Practical Problems

Discontinuities in numerical radiative transfer

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