A Two-dimensional HLLC Riemann Solver for Conservation Laws : Application to Euler and MHD Flows

In this paper we present a genuinely two-dimensional HLLC Riemann solver. On logically rectangular meshes, it accepts four input states that come together at an edge and outputs the multi-dimensionally upwinded fluxes in both directions. This work builds on, and improves, our prior work on two-dimensional HLL Riemann solvers. The HLL Riemann solver presented here achieves its stabilization by introducing a constant state in the region of strong interaction, where four one-dimensional Riemann problems interact vigorously with one another. A robust version of the HLL Riemann solver is presented here along with a strategy for introducing sub-structure in the strongly-interacting state. Introducing sub-structure turns the two-dimensional HLL Riemann solver into a two-dimensional HLLC Riemann solver. The sub-structure that we introduce represents a contact discontinuity which can be oriented in any direction relative to the mesh. The Riemann solver presented here is general and can work with any system of conservation laws. We also present a second order accurate Godunov scheme that works in three dimensions and is entirely based on the present multidimensional HLLC Riemann solver technology. The methods presented are cost-competitive with traditional higher order Godunov schemes

Multidimensional HLLE Riemann solver; Application to Euler and Magnetohydrodynamic Flows

In this work we present a general strategy for constructing multidimensional Riemann solvers with a single intermediate state, with particular attention paid to detailing the two-dimensional Riemann solver. This is accomplished by introducing a constant resolved state between the states being considered, which introduces sufficient dissipation for systems of conservation laws. Closed form expressions for the resolved fluxes are also provided to facilitate numerical implementation. The Riemann solver is proved to be positively conservative for the density variable; the positivity of the pressure variable has been demonstrated for Euler flows when the divergence in the fluid velocities is suitably restricted so as to prevent the formation of cavitation in the flow. We also focus on the construction of multidimensionally upwinded electric fields for divergence-free magnetohydrodynamical flows. A robust and efficient second order accurate numerical scheme for two and three dimensional Euler and magnetohydrodynamic flows is presented. The scheme is built on the current multidimensional Riemann solver. The number of zones updated per second by this scheme on a modern processor is shown to be cost competitive with schemes that are based on a one-dimensional Riemann solver. However, the present scheme permits larger timesteps

Low resistance n-contact for UVC LEDs by a two-step plasma etching process

The impact of plasma etching on the formation of low-resistance n-contacts on the AlGaN:Si current spreading layer during the chip fabrication of ultraviolet light-emitting diodes (UV LEDs) emitting at 265 nm is investigated. A two-step plasma etching process with a first rapid etching using BCl3/Cl2 gas mixture and a second slow etching step using pure Cl2 gas has been developed. The etching sequence provides smooth mesa side-walls and an n-AlGaN surface with reduced surface damage. Ohmic n-contacts with a contact resistivity of 3.5 10-4 Ωcm2 are obtained on Si-doped Al0.65Ga0.35N layers and the operating voltages of the UVC LEDs were reduced by 2 V for a current of 20 mA. © 2020 The Author(s). Published by IOP Publishing Ltd

Strain induced power enhancement of far-UVC LEDs on high temperature annealed AlN templates

High temperature annealed AlN/sapphire templates exhibit a reduced in-plane lattice constant compared to conventional non-annealed AlN/sapphire grown by metalorganic vapor phase epitaxy (MOVPE). This leads to additional lattice mismatch between the template and the AlGaN-based ultraviolet-C light emitting diode (UVC LED) heterostructure grown on these templates. This mismatch introduces additional compressive strain in AlGaN quantum wells resulting in enhanced transverse electric polarization of the quantum well emission at wavelengths below 235 nm compared to layer structures deposited on conventional MOVPE-grown AlN templates, which exhibit mainly transverse magnetic polarized emission. In addition, high temperature annealed AlN/sapphire templates also feature reduced defect densities leading to reduced non-radiative recombination. Based on these two factors, i.e., better outcoupling efficiency of the transverse electric polarized light and an enhanced internal quantum efficiency, the performance characteristic of far-UVC LEDs emitting at 231 nm was further improved with a cw optical output power of 3.5 mW at 150 mA

Correlated Gravitational Wave and Neutrino Signals from General-Relativistic Rapidly Rotating Iron Core Collapse

We present results from a new set of 3D general-relativistic hydrodynamic simulations of rotating iron core collapse. We assume octant symmetry and focus on axisymmetric collapse, bounce, the early postbounce evolution, and the associated gravitational wave (GW) and neutrino signals. We employ a finite-temperature nuclear equation of state, parameterized electron capture in the collapse phase, and a multi-species neutrino leakage scheme after bounce. The latter captures the important effects of deleptonization, neutrino cooling and heating and enables approximate predictions for the neutrino luminosities in the early evolution after core bounce. We consider 12-solar-mass and 40-solar-mass presupernova models and systematically study the effects of (i) rotation, (ii) progenitor structure, and (iii) postbounce neutrino leakage on dynamics, GW, and, neutrino signals. We demonstrate, that the GW signal of rapidly rotating core collapse is practically independent of progenitor mass and precollapse structure. Moreover, we show that the effects of neutrino leakage on the GW signal are strong only in nonrotating or slowly rotating models in which GW emission is not dominated by inner core dynamics. In rapidly rotating cores, core bounce of the centrifugally-deformed inner core excites the fundamental quadrupole pulsation mode of the nascent protoneutron star. The ensuing global oscillations (f~700-800 Hz) lead to pronounced oscillations in the GW signal and correlated strong variations in the rising luminosities of antineutrino and heavy-lepton neutrinos. We find these features in cores that collapse to protoneutron stars with spin periods <~ 2.5 ms and rotational energies sufficient to drive hyper-energetic core-collapse supernova explosions. Hence, joint GW + neutrino observations of a core collapse event could deliver strong evidence for or against rapid core rotation. [abridged]Comment: 29 pages, 14 figures. Replaced with version matching published versio

Simulation techniques for cosmological simulations

Modern cosmological observations allow us to study in great detail the evolution and history of the large scale structure hierarchy. The fundamental problem of accurate constraints on the cosmological parameters, within a given cosmological model, requires precise modelling of the observed structure. In this paper we briefly review the current most effective techniques of large scale structure simulations, emphasising both their advantages and shortcomings. Starting with basics of the direct N-body simulations appropriate to modelling cold dark matter evolution, we then discuss the direct-sum technique GRAPE, particle-mesh (PM) and hybrid methods, combining the PM and the tree algorithms. Simulations of baryonic matter in the Universe often use hydrodynamic codes based on both particle methods that discretise mass, and grid-based methods. We briefly describe Eulerian grid methods, and also some variants of Lagrangian smoothed particle hydrodynamics (SPH) methods.Comment: 42 pages, 16 figures, accepted for publication in Space Science Reviews, special issue "Clusters of galaxies: beyond the thermal view", Editor J.S. Kaastra, Chapter 12; work done by an international team at the International Space Science Institute (ISSI), Bern, organised by J.S. Kaastra, A.M. Bykov, S. Schindler & J.A.M. Bleeke

Scalar field induced oscillations of neutron stars and gravitational collapse

We study the interaction of massless scalar fields with self-gravitating neutron stars by means of fully dynamic numerical simulations of the Einstein-Klein-Gordon perfect fluid system. Our investigation is restricted to spherical symmetry and the neutron stars are approximated by relativistic polytropes. Studying the nonlinear dynamics of isolated neutron stars is very effectively performed within the characteristic formulation of general relativity, in which the spacetime is foliated by a family of outgoing light cones. We are able to compactify the entire spacetime on a computational grid and simultaneously impose natural radiative boundary conditions and extract accurate radiative signals. We study the transfer of energy from the scalar field to the fluid star. We find, in particular, that depending on the compactness of the neutron star model, the scalar wave forces the neutron star either to oscillate in its radial modes of pulsation or to undergo gravitational collapse to a black hole on a dynamical timescale. The radiative signal, read off at future null infinity, shows quasi-normal oscillations before the setting of a late time power-law tail.Comment: 12 pages, 13 figures, submitted to Phys. Rev.

A New Open-Source Code for Spherically-Symmetric Stellar Collapse to Neutron Stars and Black Holes

We present the new open-source spherically-symmetric general-relativistic (GR) hydrodynamics code GR1D. It is based on the Eulerian formulation of GR hydrodynamics (GRHD) put forth by Romero-Ibanez-Gourgoulhon and employs radial-gauge, polar-slicing coordinates in which the 3+1 equations simplify substantially. We discretize the GRHD equations with a finite-volume scheme, employing piecewise-parabolic reconstruction and an approximate Riemann solver. GR1D is intended for the simulation of stellar collapse to neutron stars and black holes and will also serve as a testbed for modeling technology to be incorporated in multi-D GR codes. Its GRHD part is coupled to various finite-temperature microphysical equations of state in tabulated form that we make available with GR1D. An approximate deleptonization scheme for the collapse phase and a neutrino-leakage/heating scheme for the postbounce epoch are included and described. We also derive the equations for effective rotation in 1D and implement them in GR1D. We present an array of standard test calculations and also show how simple analytic equations of state in combination with presupernova models from stellar evolutionary calculations can be used to study qualitative aspects of black hole formation in failing rotating core-collapse supernovae. In addition, we present a simulation with microphysical EOS and neutrino leakage/heating of a failing core-collapse supernova and black hole formation in a presupernova model of a 40 solar mass zero-age main-sequence star. We find good agreement on the time of black hole formation (within 20%) and last stable protoneutron star mass (within 10%) with predictions from simulations with full Boltzmann neutrino radiation hydrodynamics.Comment: 25 pages, 6 figures, 2 appendices. Accepted for publication to the Classical and Quantum Gravity special issue for MICRA2009. Code may be downloaded from http://www.stellarcollapse.org Update: corrected title, small modifications suggested by the referees, added source term derivation in appendix