An adaptive mesh, GPU-accelerated, and error minimized special relativistic hydrodynamics code

We deal with the numerical approximation of the complex structure in special relativistic hydrodynamics (SRHD) when the system is closed with a non-convex equation of state (EOS). We consider a recently introduced phenomenological EOS (Ibanez et al. in MNRAS 476:1100, 2018) that mimics the loss of classical behavior when the fluid enters into a non-convex—thermodynamically—region in the relativistic regime. We introduce a flux formulation to approximate the solution of Riemann problems in SRHD such that the non-classical dynamics is detected and well resolved. We also design a strategy to recover primitive variables based on iterative procedures and present a detailed analysis providing a sufficient condition to ensure convergence. We propose a set of Riemann problems in one and two dimensions including blast waves, colliding slabs and expanding slabs, illustrating the strong complex dynamics arising in non-convex SRHD.

To study the dynamics of relativistic flows in astrophysical objects such as radio jets, we have developed a new special relativistic hydrodynamic (RHD) code based on the weighted essentially non-oscillatory (WENO) scheme, a high-order finite difference scheme. The code includes different WENO versions, and high-order time integration methods such as the 4th-order accurate Runge-Kutta (RK4) and strong stability preserving RK (SSPRK), as well as the equations of state (EOSs) that closely approximate the EOS of the single-component perfect gas in relativistic regime. Additionally, it is optimized for the reproduction of complex structures in multi-dimensional flows, and implements a modification of eigenvalues for the acoustic modes to effectively control carbuncle instability. As the first application of the code, we have simulated ultra-relativistic jets of FR II radio galaxies, and studied the nonlinear flow structures, such as shocks, velocity shear, and turbulence, through large-scale.

Viscosity and magnetic fields drive differentially rotating stars toward uniform rotation, which has important consequences in many astrophysical contexts. For example, merging binary neutron stars can form a "hypermassive" remnant, i.e. a differentially rotating star with a mass greater than the maximum allowed by uniform rotation. The removal of the centrifugal support provided by differential rotation can lead to delayed collapse of the remnant to a black hole, accompanied by a burst of gravitational radiation. Both magnetic fields and viscosity alter the structure of differentially rotating stars on secular timescales, making numerical tracking of the evolution difficult. Here, we present the first simulations of rapidly rotating stars with shear viscosity in full general relativity. We self-consistently include viscosity in our relativistic hydrodynamic code to solve the relativistic Navier-Stokes equations both in axisymmetry and in full 3+1 dimensions. In axisymmetry, we follow secular evolution with high resolution over dozens of rotation periods (thousands of M). We find that viscosity operating in a hypermassive star generically leads to the formation of a compact, uniformly rotating core surrounded by a low-density disk. These uniformly rotating cores are often, but not always, unstable to gravitational collapse. In the unstable cases, we follow the collapse and determine the mass and the spin of the final black hole and ambient disk. In all cases studied, the rest mass of the resulting disk is found to be 10-20% of the original star, whether surrounding a uniformly rotating core or a rotating black hole. This study foreshadows more detailed, future simulations of secular processes, including magnetic effects, in relativistic stars.

Relativistic hydrodynamic simulations play a key role in exploring the QGP bulk property and the QCD phase transition in analyses of high-energy heavy-ion collisions at RHIC and LHC. For the quantitative understanding of the QGP property, hydrodynamic calculation with high-precision is important. Using a Riemann solver based on the two-shock approximation, we construct a new 3+1 dimensional relativistic viscous hydrodynamics code. The new hydrodynamics algorithm has less numerical viscosity, which is important to discuss the physical viscosities at RHIC and LHC. For one of applications of the new hydrodynamics code, we argue the possible development of Kelvin-Helmholtz instability in high-energy heavy-ion collisions.

A canonical approach to Cherenkov radiation in the presence of a magnetodielectric medium is presented in classical, nonrelativistic and relativistic quantum regimes. The equations of motion for the canonical variables are solved explicitly for both positive and negative times. Maxwell and related constitute equations are obtained. In the large-time limit, the vector potential operator is found and expressed in terms of the medium operators. The energy loss of a charged particle, emitted in the form of radiation, in finite temperature is calculated. A Dirac equation concerning the relativistic motion of the particle in presence of the magnetodielectric medium is derived and the relativistic Cherenkov radiation at zero and finite temperature is investigated. Finally, it is shown that the Cherenkov radiation in nonrelativistic and relativistic quantum regimes, unlike its classical counterpart, introduces automatically a cutoff for higher frequencies beyond which the power of radiation emission is zero.

High-order accurate entropy stable adaptive moving mesh finite difference schemes for special relativistic (magneto)hydrodynamics

Adaptive kinetic-fluid solvers for heterogeneous computing architectures

We present the results of an investigation of the dredge-up and mixing during the merger of two white dwarfs (WDs) with different chemical compositions by conducting hydrodynamic simulations of binary mergers for three representative mass ratios. In all the simulations, the total mass of the two WDs is ≲1.0 M ⊙. Mergers involving a CO and a He WD have been suggested as a possible formation channel for R Coronae Borealis (RCB)–type stars, and we are interested in testing if such mergers lead to conditions and outcomes in agreement with observations. Even if the conditions during the merger and subsequent nucleosynthesis favor the production of 18O, the merger must avoid dredging up large amounts of 16O, or else it will be difficult to produce sufficient 18O to explain the oxygen ratio observed to be of order unity. We performed a total of nine simulations using two different grid-based hydrodynamics codes using fixed and adaptive meshes and one smooth particle hydrodynamics (SPH) code. We find that in most of the simulations, >10−2 M ⊙ of 16O is indeed dredged up during the merger. However, in SPH simulations where the accretor is a hybrid He/CO WD with a ∼0.1 M ⊙ layer of helium on top, we find that no 16O is being dredged up, while in the q = 0.8 simulation <10−4 M ⊙ of 16O has been brought up, making a WD binary consisting of a hybrid CO/He WD and a companion He WD an excellent candidate for the progenitor of RCB stars.

Transport equations in moving material Part I: Neutrons and photons

Charged particle dynamics in Reissner–Nordström–Tangherlini spacetime

In order to improve the finite-element modeling of macroscopic eddy currents (associated with motion and/or a time-varying electrical excitation), an original error criterion for adaptive meshing, based on a local power conservation, is proposed. Then, the importance of the order element in the error computation is investigated. Finally, the criterion is coupled to a ldquobubblerdquo mesh generator, and an adaptive meshing of a 2D induction heating case is performed.

In this paper, we use the conventional quantum hydrodynamics (QHD) model in combination with the Sagdeev pseudopotential method to explore the effects of Thomas-Fermi nonuniform electron distribution, Coulomb interactions, electron exchange, and ion correlation on the large-amplitude nonlinear soliton dynamics in Fermi-Dirac plasmas. It is found that in the presence of strong interactions, significant differences in nonlinear wave dynamics of Fermi-Dirac plasmas in the two distinct regimes of nonrelativistic and relativistic degeneracies exist. Furthermore, it is remarked that first-order corrections due to such interactions (which are proportional to the fine-structure constant) are more significant on soliton characteristics (particularly the amplitude) in the nonrelativistic plasma degeneracy regime rather than the relativistic one. In the relativistic degeneracy regime, however, these effects become less important and the electron quantum-tunneling and Pauli-exclusion dominate the nonlinear wave dynamics. Hence, application of non-interacting Fermi-Dirac QHD model to study the nonlinear wave dynamics in quantum plasmas, such as in compact stars is most appropriate for the relativistic degeneracy regime rather than nonrelativistic one.

A new adaptive hybrid mesh generation method is presented in this paper to deal with planar domains of arbitrary shapes. The tree decomposition is governed by a size function in R 2 . Our main goal is to e‐ciently produce an adequate mesh for Reynolds-averaged Navier-Stokes numerical simulations of turbulent viscous ∞ow. The result is an adaptive quad-dominant hybrid mesh ready for the application of agglomeration multigrid methods. Several application examples are provided to show the strength of this approach. A simple optimization step is required and enables the extension of this method to 3D in a straight forward manner.

We conjecture that the random walk and the corresponding diffusion in the relativistic velocity space is an adequate method for describing the acceleration process in relativistic jets. Considering a simple toy model, the main features of diffusion in the velocity space are demonstrated in both non-relativistic and relativistic regimes.

Using our developed new relativistic viscous hydrodynamics code, we investigate the temperature dependence of shear and bulk viscosities from comparison with the ALICE data: single particle spectra and collective flows of Pb+Pb $\sqrt{s_{\rm NN}}=2.76$ TeV collisions at the Large Hadron Collider. We find that from the comprehensive analyses of centrality dependence of single particle spectra and collective flows we can extract detailed information on the quark-gluon plasma bulk property, without the information being smeared by the final state interactions.