Mapping Initial Hydrostatic Models in Godunov Codes

Zingale, M.; Dursi, L. J.; ZuHone, John; Calder, A. C.; Fryxell, B.; Plewa, T.; Truran, J. W.; Caceres, A.; Olson, K.; Ricker, P. M.; Riley, Katherine; Rosner, R.; Siegel, A.; Timmes, F. X.; Vladimirova, Natalia

doi:10.1086/342754

Cited by 109 publications

(111 citation statements)

References 18 publications

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“…For Rusanov or local LaxFriedrichs type Riemann solvers, Käppeli et al (2011) have subtracted the gradients induced by gravity in the dissipative flux terms. Yet another strategy for finite volume schemes is to introduce a subgrid model which incorporates the stationary state into the reconstruction process, see, e.g., Freytag et al (2012), Mellema et al (1991), Zingale et al (2002). Greenberg & Leroux (1996) introduced the concept of a well-balanced scheme, i.e., a scheme which satisfies exactly a discrete equivalent of an underlying stationary state.…”

Section: Introductionmentioning

confidence: 99%

A well-balanced finite volume scheme for the Euler equations with gravitation

Käppeli

Mishra

2016

A&A

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Context. Many problems in astrophysics feature flows which are close to hydrostatic equilibrium. However, standard numerical schemes for compressible hydrodynamics may be deficient in approximating this stationary state, where the pressure gradient is nearly balanced by gravitational forces. Aims. We aim to develop a second-order well-balanced scheme for the Euler equations. The scheme is designed to mimic a discrete version of the hydrostatic balance. It therefore can resolve a discrete hydrostatic equilibrium exactly (up to machine precision) and propagate perturbations, on top of this equilibrium, very accurately. Methods. A local second-order hydrostatic equilibrium preserving pressure reconstruction is developed. Combined with a standard central gravitational source term discretization and numerical fluxes that resolve stationary contact discontinuities exactly, the wellbalanced property is achieved. Results. The resulting well-balanced scheme is robust and simple enough to be very easily implemented within any existing computer code that solves time explicitly or implicitly the compressible hydrodynamics equations. We demonstrate the performance of the well-balanced scheme for several astrophysically relevant applications: wave propagation in stellar atmospheres, a toy model for core-collapse supernovae, convection in carbon shell burning, and a realistic proto-neutron star.

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Section: Introductionmentioning

confidence: 99%

A well-balanced finite volume scheme for the Euler equations with gravitation

Käppeli

Mishra

2016

A&A

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“…In addition to conservation laws, some physical processes, such as nuclear burning, are very sensitive to temperature, so errors in mapping can lead to very different outcomes for the simulations, including altering the nucleosynthesis and energetics of SNe. [46] has examined mapping 1D profiles to 2D or 3D meshes under a hydro equilibrium status and [47] has developed a new mapping scheme to conservatively map the 1D initial conditions onto multidimensional zones.…”

Section: Mappingmentioning

confidence: 99%

Supernovae at the cosmic dawn

Chen

2014

Int. J. Mod. Phys. D

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Modern cosmological simulations predict that the first generation of stars formed with a mass scale around 100 M about 300 − 400 million years after the Big Bang. When the first stars reached the end of their lives, many of them might have died as energetic supernovae that could have significantly affected the early Universe via injecting large amounts of energy and metals into the primordial intergalactic medium. In this paper, we review the current models of the first supernovae by discussing on the relevant background physics, computational methods, and the latest results.

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“…Consider an ideal gas with γ = 1.4 and the linear gravitational field φ x = φ y = g. The isothermal equilibrium state under consideration takes the form of 6) with the parameters ρ 0 = 1.21, p 0 = 1 and g = 1.…”

Section: Two Dimensional Isothermal Equilibrium Solutionmentioning

confidence: 99%

“…A Riemann problem is introduced in the center of each grid cell such that the flux difference exactly cancels the source term. Zingale et al [6] investigated the process of mapping an astrophysical initial model from a stellar evolution code onto the computational grid of an explicit code while maintaining hydrostatic equilibrium. A different strategy for the construction of well-balanced discretizations with respect to dominant hydrostatics has been proposed by Botta et al [5] for the nearly hydrostatic flows belonging to a certain class of solutions.…”

Section: Introductionmentioning

confidence: 99%

High Order Well-balanced WENO Scheme for the Gas Dynamics Equations under Gravitational Fields

Xing¹,

Shu²

2011

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The gas dynamics equations, coupled with a static gravitational field, admit the hydrostatic balance where the flux produced by the pressure is exactly canceled by the gravitational source term. Many astrophysical problems involve the hydrodynamical evolution in a gravitational field, therefore it is essential to correctly capture the effect of gravitational force in the simulations. Improper treatment of the gravitational force can lead to a solution which either oscillates around the equilibrium, or deviates from the equilibrium after a long time run. In this paper we design high order well-balanced finite difference WENO schemes to this system, which can preserve the hydrostatic balance state exactly and at the same time can maintain genuine high order accuracy. Numerical tests are performed to verify high order accuracy, well-balanced property, and good resolution for smooth and discontinuous solutions. Keywords TR-2011-279. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSOR/MONITOR'S ACRONYM(S) SPONSOR/MONITOR'S REPORT NUMBER(S) DISTRIBUTION/AVAILABILITY STATEMENTApproved for public release; distribution unlimited SUPPLEMENTARY NOTES ABSTRACTThe gas dynamics equations, coupled with a static gravitational field, admit the hydrostatic balance where the flux produced by the pressure is exactly canceled by the gravitational source term. Many astrophysical problems involve the hydrodynamical evolution in a gravitational field, therefore it is essential to correctly capture the effect of gravitational force in the simulations. Improper treatment of the gravitational force can lead to a solution which either oscillates around the equilibrium, or deviates from the equilibrium after a long time run. In this paper we design high order well-balanced finite difference WENO schemes to this system, which can preserve the hydrostatic balance state exactly and at the same time can maintain genuine high order accuracy. Numerical tests are performed to verify high order accuracy, well-balanced property, and good resolution for smooth and discontinuous solutions.

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Mapping Initial Hydrostatic Models in Godunov Codes

Cited by 109 publications

References 18 publications

A well-balanced finite volume scheme for the Euler equations with gravitation

A well-balanced finite volume scheme for the Euler equations with gravitation

Supernovae at the cosmic dawn

High Order Well-balanced WENO Scheme for the Gas Dynamics Equations under Gravitational Fields

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