Mixing Sinc kernels to improve interpolations in smoothed particle hydrodynamics without pairing instability

The smoothed particle hydrodynamics technique strongly relies on the proper choice of interpolating functions. In this work, we revisit and extend the main properties of a family of interpolators called $Sinc~kernels$ and compare them with those of the widely used family of Wendland kernels. We show that a linear combination of low and high-order Sinc kernels generates good quality interpolators, which are resistant to the pairing instability while keeping good sampling properties in a wide range of neighbor interpolating points, $60\le n_b\le 400$. We show that a particular case of this linear mix of Sincs produces a well-balanced and robust kernel, that improves previous results in the Gresho-Chan vortex experiment even when the number of neighbors is not large, while yielding a good convergence rate. Although such a mixing technique is ideally suited for Sinc kernels owing to their excellent flexibility, it can be easily applied to other interpolating families such as the B-splines and Wendland kernels.Comment: 13 pages, 14 figures, 4 tables, submitted to MNRA

Building initial models of rotating white dwarfs with SPH

A general procedure to build self-gravitational, rotating equilibrium structures with the Smoothed Particle Hydrodynamics (SPH) technique does not exist. In particular, obtaining stable rotating configurations for white dwarf (WD) stars is currently a major drawback of many astrophysical simulations. Rotating WDs with low internal temperatures are connected with both, explosive and implosive scenarios such as type Ia supernova explosions or neutron stars formation. Simulations of these events with SPH codes demand stable enough particle configurations as initial models. In this work we have developed and tested a relaxation method to obtain equilibrium configurations of rotating WDs. This method is straightforward and takes advantage of the excellent mass and angular momentum conservation properties of the SPH technique. Although we focus on rigid rotation and its potential applications to several Type Ia supernova scenarios, we also show that our proposal is also able to provide good initial models in differential rotation, which has the potential to benefit many other types of simulations where rotation plays a capital role, like disk evolution and stellar formation.Peer ReviewedPostprint (published version

Integral SPH: Connecting the partition of unit to accurate gradient estimation

AYA2017-86274-P Del enfriamiento a las explosiones: la física de los objetos compactosPostprint (published version

Surface and core detonations in rotating white dwarfs

The feasibility of the double detonation mechanism—surface helium detonation followed by complete carbon detonation of the core—in a rotating white dwarf with mass ;1Me is studied using three-dimensional hydrodynamic simulations. A rapid rigid rotation of the white dwarf was assumed, so that its initial spherical geometry is considerably distorted. Unlike spherically symmetric models, we found that when helium ignition is located far from the spinning axis, the detonation fronts converge asynchronically at the antipodes of the ignition point. Nevertheless, the detonation of the carbon core still remains as the most probable outcome. The detonation of the core gives rise to a strong explosion, matching many of the basic observational constraints of Type Ia supernovae (SNe Ia). We conclude that the double detonation mechanism also works when the white dwarf is rapidly rotating. These results provide further evidence for the viability of sub-Chandrasekhar-mass models as well as some double degenerate models (those having some helium fuel at the merging moment), making them appealing channels for the production of SN Ia events.Peer ReviewedPostprint (published version

Simulation of X-ray Bursts and Superbursts

Regular bursts have been observed in binary systems containing a neutron star with an accretion flow of matter from the companion star. These bursts are so-called type I X-ray bursts and occur due to thermonuclear explosions in the accreted shell of the neutron stars. Observations have shown that after thousands of X-ray bursts a rare superburst event may take place. These superbursts are thought to be triggered by unstable carbon ignition from the accumulated ashes of the previous X-ray bursts. One of our aims is to produce a self-consistent superburst, for which the amount of the remaining 12C in the ashes is a crucial factor. Furthermore, we investigate the influence of the crustal heating on the behaviour of X-ray bursts and on the composition of their ashes

A moderately-sized nuclear network to assist multi-D hydrodynamic simulations of supernova explosions

A key ingredient in any numerical study of supernova explosions is the nuclear network routine that is coupled with the hydrodynamic simulation code. When these studies are performed in more than one dimension, the size of the network is severely limited by computational issues. In this work, we propose a nuclear network (net87) which is close to one hundred nuclei and could be appropriate to simulate supernova explosions in multidimensional studies. One relevant feature is that electron and positron captures on free protons and neutrons have been incorporated to the network. Such addition allows for a better track of both, the neutronized species and the gas pressure. A second important feature is that the reactions are implicitly coupled with the temperature, which enhances the stability in the nuclear statistical equilibrium (NSE) regime. Here we analyze the performance of net87 in light of both: the computational overhead of the algorithm and the outcome in terms of the released nuclear energy and produced yields in typical Type Ia Supernova conditions.Postprint (published version

Integral smoothed particle hydrodynamics with an improved partition of unit and a better track of contact discontinuities

The correct evaluation of gradients is at the cornerstone of the smoothed particle hydrodynamics (SPH) technique. Using an integral approach to estimate gradients has proven to enhance accuracy substantially. Such approach retains the Lagrangian structure of SPH equations and is fully conservative. In this paper we study, among other things, the connection between the choice of the volume elements (VEs), which enters in the SPH summations, and the accuracy in the gradient estimation within the integral approach scheme (ISPH). A new kind of VEs are proposed which improve the partition of unit and are fully compatible with the Lagrangian formulation of SPH, including the grad-h corrections. Using analytic considerations, simple static toy models in 1D, and a few full 3D test cases, we show that any improvement in the partition of unit also leads to a better calculation of gradients when the integral approach is used jointly. Additionally, we propose a simple-to-implement variant of the ISPH scheme which is more adequate to handle sharp density contrasts.Comment: 29 pages, 17 figures, submitted to Journal of Computational Physic

Smoothed particle hydrodynamics: checking a tensor approach to calculating gradients

Postprint (published version

A New Kilohertz Gravitational-Wave Feature from Rapidly Rotating Core-Collapse Supernovae

We present self-consistent three-dimensional core-collapse supernova simulations of a rotating $20M_\odot$ progenitor model with various initial angular velocities from $0.0$ to $4.0$ rad s$^{-1}$ using a smoothed particle hydrodynamics code, SPHYNX, and a grid-based hydrodynamics code, FLASH. We identify two strong gravitational-wave features, with peak frequencies of $\sim300$ Hz and $\sim1.3$ kHz in the first $100$ ms postbounce. We demonstrate that these two features are associated with the $m=1$ deformation from the proto-neutron star (PNS) modulation induced by the low-$T/|W|$ instability, regardless of the simulation code. The $300$ Hz feature is present in models with an initial angular velocity between $1.0$ and $4.0$ rad s$^{-1}$, while the $1.3$ kHz feature is present only in a narrower range, from $1.5$ to $3.5$ rad s$^{-1}$. We show that the $1.3$ kHz signal originates from the high-density inner core of the PNS, and the $m=1$ deformation triggers a strong asymmetric distribution of electron anti-neutrinos. In addition to the $300$ Hz and $1.3$ kHz features, we also observe one weaker but noticeable gravitational-wave feature from higher-order modes in the range between $1.5$ and $3.5$ rad s$^{-1}$. Its peak frequency is around $800$ Hz initially and gradually increases to $900-1000$ Hz. Therefore, in addition to the gravitational bounce signal, the detection of the $300$ Hz, $1.3$ kHz, the higher-order mode, and even the related asymmetric emission of neutrinos, could provide additional diagnostics to estimate the initial angular velocity of a collapsing core.Comment: 20 pages, 14 figures,. Accepted for publication in the Astrophysical Journa

Equalizing resolution in smoothed-particle hydrodynamics calculations using self-adaptive sinc kernels

The smoothed-particle hydrodynamics (SPH) technique is a numerical method for solving gas-dynamical problems. It has been applied to simulate the evolution of a wide variety of astrophysical systems. The method has a second-order accuracy, with a resolution that is usually much higher in the compressed regions than in the diluted zones of the fluid. In this work, we propose and check a scheme to balance and equalize the resolution of SPH between high- and low-density regions. This method relies on the versatility of a family of interpolators called Sinc kernels, which allows increasing the interpolation quality by varying only a single parameter (the exponent of the Sinc function). The scheme is checked and validated through a number of numerical tests, from standard one-dimensional Riemann problems in shock tubes, to multidimensional simulations of explosions, hydrodynamic instabilities and the collapse of a sun-like polytrope. The analysis of the hydrodynamical simulations suggests that the scheme devised to equalizing accuracy improves the treatment of the post-shock regions and, in general, of the rarefacted zones of fluids while causing no harm to the growth of hydrodynamic instabilities. The method is robust and easy to implement with a low computational overload. It conserves mass, energy, and momentum and reduces to the standard SPH scheme in regions of the fluid that have smooth density gradients.Comment: 29 pages, 18 figures, accepted by A&