A Jacobian-free Newton-Krylov method for time-implicit multidimensional hydrodynamics

Viallet, Maxime; Goffrey, T.; Baraffe, I.; Folini, Doris; Geroux, C.; Попов, М. В.; Pratt, J.; Walder, Rolf

doi:10.1051/0004-6361/201527339

Cited by 44 publications

(46 citation statements)

References 16 publications

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“…This simplified treatment might be inadequate in some cases. Ongoing studies aim at improving the theoretical modeling and understanding of convection in stellar interiors (e.g., Meakin & Arnett 2007;Arnett et al 2009Arnett et al , 2015Viallet et al 2013Viallet et al , 2015Viallet et al , 2016.…”

Section: Introductionmentioning

confidence: 99%

Angular Momentum Fluctuations in the Convective Helium Shell of Massive Stars

Gilkis

Soker

2016

ApJ

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We find significant fluctuations of angular momentum within the convective helium shell of a pre-collapse massive star-a core-collapse supernova progenitor-that may facilitate the formation of accretion disks and jets that can explode the star. The convective flow in our model of an evolved =  M M 15 ZAMS star, computed using the subsonic hydrodynamic solver MAESTRO, contains entire shells with net angular momentum in different directions. This phenomenon may have important implications for the late evolutionary stages of massive starsand for the dynamics of corecollapse.

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Section: Introductionmentioning

confidence: 99%

Angular Momentum Fluctuations in the Convective Helium Shell of Massive Stars

Gilkis

Soker

2016

ApJ

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“…4 of Viallet et al (2016). Viallet et al (2016) show that MUSIC is able to produce consistent results for a range of Mach numbers, 10 −1 ≤ M s ≤ 10 −6 .…”

Section: Effect Of Grid Sizementioning

confidence: 84%

“…However in this work, we adjust p 0 so that the initial peak Mach number is M s = 0.28, as in DFGY2007. Therefore, in addition to verifying MUSIC through comparison to a range of ILES, conventional LES, and DNS simulations, we can also investigate possible compressive effects through comparison to Viallet et al (2016).…”

Section: Problem Descriptionmentioning

confidence: 99%

“…The large time-step facilitated by the application of this preconditioner allows the structure to settle towards equilibrium efficiently, without the need of explicit damping. We have not tried to fine-tune the parameters of our solver (see Viallet et al 2016) to reach lower velocities. We consider these results and the convergence toward a hydrostatic equilibrium state as satisfactory given the extremely low Mach numbers reached at the end of the relaxation process.…”

Section: Hydrostatic Equilibrium Under Realistic Stellar Conditionsmentioning

confidence: 99%

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Benchmarking the Multidimensional Stellar Implicit Code MUSIC

Goffrey

Pratt

Viallet

et al. 2017

A&A

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We present the results of a numerical benchmark study for the MUltidimensional Stellar Implicit Code (MUSIC) based on widely applicable two-and three-dimensional compressible hydrodynamics problems relevant to stellar interiors. MUSIC is an implicit large eddy simulation code that uses implicit time integration, implemented as a Jacobian-free Newton Krylov method. A physics based preconditioning technique which can be adjusted to target varying physics is used to improve the performance of the solver. The problems used for this benchmark study include the Rayleigh-Taylor and Kelvin-Helmholtz instabilities, and the decay of the Taylor-Green vortex. Additionally we show a test of hydrostatic equilibrium, in a stellar environment which is dominated by radiative effects. In this setting the flexibility of the preconditioning technique is demonstrated. This work aims to bridge the gap between the hydrodynamic test problems typically used during development of numerical methods and the complex flows of stellar interiors. A series of multidimensional tests were performed and analysed. Each of these test cases was analysed with a simple, scalar diagnostic, with the aim of enabling direct code comparisons. As the tests performed do not have analytic solutions, we verify MUSIC by comparing it to established codes including ATHENA and the PENCIL code. MUSIC is able to both reproduce behaviour from established and widely-used codes as well as results expected from theoretical predictions. This benchmarking study concludes a series of papers describing the development of the MUSIC code and provides confidence in future applications.

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“…In the reduced speed of sound technique (RSST) and related methods, the speed of sound is artificially reduced by including a suitable scaling factor in the continuity equation, reducing the restriction on the size of the time step (Rempel 2005;Hotta et al 2012;Wang et al 2015;Takeyama et al 2017;Iijima et al 2019). Finally, there are fully implicit time integration codes for the compressible Euler equations (Viallet et al 2011;Kifonidis & Müller 2012;Viallet et al 2015;Goffrey et al 2017). The MUSIC code uses fully implicit time integration for the compressible Euler equations, which therefore allows for arbitrarily large time steps.…”

Section: Introductionmentioning

confidence: 99%

MAESTROeX: A Massively Parallel Low Mach Number Astrophysical Solver

Fan¹,

Nonaka²,

Almgren³

et al. 2019

JOSS

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We present MAESTROeX, a massively parallel solver for low Mach number astrophysical flows. The underlying low Mach number equation set allows for efficient, long-time integration for highly subsonic flows compared to compressible approaches. MAESTROeX is suitable for modeling full spherical stars as well as well as planar simulations of dynamics within localized regions of a star, and can robustly handle several orders of magnitude of density and pressure stratification. Previously, we have described the development of the predecessor of MAESTROeX, called MAESTRO, in a series of papers. Here, we present a new, greatly simplified temporal integration scheme that retains the same order of accuracy as our previous approaches. We also explore the use of alternative spatial mapping of the one-dimensional base state onto the full Cartesian grid. The code leverages the new AMReX software framework for block-structured adaptive mesh refinement (AMR) applications, allowing for scalability to large fractions of leadership-class machines. Using our previous studies on the convective phase of single-degenerate progenitor models of Type Ia supernovae as a guide, we characterize the performance of the code and validate the new algorithmic features. Like MAESTRO, MAESTROeX is fully open source.

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A Jacobian-free Newton-Krylov method for time-implicit multidimensional hydrodynamics

Cited by 44 publications

References 16 publications

Angular Momentum Fluctuations in the Convective Helium Shell of Massive Stars

Angular Momentum Fluctuations in the Convective Helium Shell of Massive Stars

Benchmarking the Multidimensional Stellar Implicit Code MUSIC

MAESTROeX: A Massively Parallel Low Mach Number Astrophysical Solver

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