A Physical-Constraint-Preserving Finite Volume WENO Method for Special Relativistic Hydrodynamics on Unstructured Meshes

This paper presents a highly robust third-order accurate finite volume weighted essentially non-oscillatory (WENO) method for special relativistic hydrodynamics on unstructured triangular meshes. We rigorously prove that the proposed method is physical-constraint-preserving (PCP), namely, always preserves the positivity of the pressure and the rest-mass density as well as the subluminal constraint on the fluid velocity. The method is built on a highly efficient compact WENO reconstruction on unstructured meshes, a simple PCP limiter, the provably PCP property of the Harten--Lax--van Leer flux, and third-order strong-stability-preserving time discretization. Due to the relativistic effects, the primitive variables (namely, the rest-mass density, velocity, and pressure) are highly nonlinear implicit functions in terms of the conservative variables, making the design and analysis of our method nontrivial. To address the difficulties arising from the strong nonlinearity, we adopt a novel quasilinear technique for the theoretical proof of the PCP property. Three provable convergence-guaranteed iterative algorithms are also introduced for the robust recovery of primitive quantities from admissible conservative variables. We also propose a slight modification to an existing WENO reconstruction to ensure the scaling invariance of the nonlinear weights and thus to accommodate the homogeneity of the evolution operator, leading to the advantages of the modified WENO reconstruction in resolving multi-scale wave structures. Extensive numerical examples are presented to demonstrate the robustness, expected accuracy, and high resolution of the proposed method.Comment: 56 pages, 18 figure

Anomalous wave structure in magnetized materials described by non-convex equations of state

Agraïments: Institute for Pure and Applied Mathematics (UCLA) 2012 program on "Computational Methods in High Energy Density Plasmas.We analyze the anomalous wave structure appearing in flow dynamics under the influence of magnetic field in materials described by non-ideal equations of state. We consider the system of magnetohydrodynamics equations closed by a general equation of state (EOS) and propose a complete spectral decomposition of the fluxes that allows us to derive an expression of the nonlinearity factor as the mathematical tool to determine the nature of the wave phenomena. We prove that the possible formation of non-classical wave structure is determined by both the thermodynamic properties of the material and the magnetic field as well as its possible rotation. We demonstrate that phase transitions induced by material properties do not necessarily imply the loss of genuine nonlinearity of the wavefields as is the case in classical hydrodynamics. The analytical expression of the nonlinearity factor allows us to determine the specific amount of magnetic field necessary to prevent formation of complex structure induced by phase transition in the material. We illustrate our analytical approach by considering two non-convex EOS that exhibit phase transitions and anomalous behavior in the evolution. We present numerical experiments validating the analysis performed through a set of one-dimensional Riemann problems. In the examples we show how to determine the appropriate amount of magnetic field in the initial conditions of the Riemann problem to transform a thermodynamic composite wave into a simple nonlinear wave

Characteristic Evolution and Matching

I review the development of numerical evolution codes for general relativity based upon the characteristic initial value problem. Progress in characteristic evolution is traced from the early stage of 1D feasibility studies to 2D axisymmetric codes that accurately simulate the oscillations and gravitational collapse of relativistic stars and to current 3D codes that provide pieces of a binary black hole spacetime. Cauchy codes have now been successful at simulating all aspects of the binary black hole problem inside an artificially constructed outer boundary. A prime application of characteristic evolution is to extend such simulations to null infinity where the waveform from the binary inspiral and merger can be unambiguously computed. This has now been accomplished by Cauchy-characteristic extraction, where data for the characteristic evolution is supplied by Cauchy data on an extraction worldtube inside the artificial outer boundary. The ultimate application of characteristic evolution is to eliminate the role of this outer boundary by constructing a global solution via Cauchy-characteristic matching. Progress in this direction is discussed.Comment: New version to appear in Living Reviews 2012. arXiv admin note: updated version of arXiv:gr-qc/050809

Core-Collapse Supernova Simulations With Spectral Two-Moment Neutrino Transport

The primary focus of this dissertation is to develop a next-generation, state-of-the-art neutrino kinetics capability that will be used in the context of the next-generation, state-of-the-art core-collapse supernova (CCSN) simulation frameworks \thornado\ and \FLASH.\index{CCSN} \thornado\ is a \textbf{t}oolkit for \textbf{h}igh-\textbf{or}der \textbf{n}eutrino-r\textbf{ad}iation hydr\textbf{o}dynamics, which is a collection of modules that can be incorporated into a simulation code/framework, such as \FLASH, together with a nuclear equation of state (EOS)\index{EOS} library, such as the \WeakLib\ EOS tables. The first part of this work extends the \WeakLib\ code to compute neutrino interaction rates from~\cite{Bruenn_1985} and produce corresponding opacity tables.\index{Bruenn 1985} The processes of emission, absorption, scattering of neutrinos from nucleons and nuclei, neutrino--electron scattering, and neutrino pair production and annihilation are included. The second part of this dissertation builds the special-relativity-corrected (\Ov) neutrino radiation module in \thornado, based on the spectral two-moment method.\index{\Ov} This part of the work involved studying the accuracy, efficiency, and robustness of the numerical solver. We propose a special kind of implicit-explicit scheme, PDARSs, based on efficiency, diffusion accuracy, and physics-preserving (positivity-preserving and realizability-preserving) requirements. \index{PD-ARS} Emission, absorption, scattering of neutrinos from nucleons and nuclei, neutrino--electron scattering, and neutrino pair production and annihilation are included as neutrino--matter couplings. The third part of this work builds interfaces between \FLASH\ and \thornado, \FLASH\ and \WeakLib, and \thornado\ and \WeakLib\ for simulations with the \FLASH\ hydrodynamics module, \WeakLib\ EOS module, and \thornado\ neutrino kinetics module. This part of the work includes data mapping between finite-volume grids and finite-element grids, time-step balancing between hydrodynamics time steps and radiation transport time steps, and GPU enhancement. The fourth part of this work makes a detailed comparison of the results of a spherically symmetric simulation performed by \FLASH+\thornado\ with the result of the \chimera\ code, which is a sophisticated, mature, and evolving code with spectral flux-limited diffusion (one-moment) neutrino kinetics and improved input physics~\citep{bruenn_etal_2020}. This part of the work demonstrates the ability of \FLASH+\thornado\ to perform CCSN simulations and quantifies the potential differences between the two codes caused by the different neutrino kinetics treatments, as well as other differences. Supported by all of the above work, spherically symmetric CCSN simulations with spectral two-moment neutrino kinetics were performed for three low-mass progenitors of 9-, 10-, and 11-Solar-mass (\solarmass) from~\cite{sukhbold_etal_2016}

Beam-Induced Damage Mechanisms and their Calculation

The rapid interaction of highly energetic particle beams with matter induces dynamic responses in the impacted component. If the beam pulse is sufficiently intense, extreme conditions can be reached, such as very high pressures, changes of material density, phase transitions, intense stress waves, material fragmentation and explosions. Even at lower intensities and longer time-scales, significant effects may be induced, such as vibrations, large oscillations, and permanent deformation of the impacted components. These lectures provide an introduction to the mechanisms that govern the thermomechanical phenomena induced by the interaction between particle beams and solids and to the analytical and numerical methods that are available for assessing the response of impacted components. An overview of the design principles of such devices is also provided, along with descriptions of material selection guidelines and the experimental tests that are required to validate materials and components exposed to interactions with energetic particle beams.Comment: 69 pages, contribution to the 2014 Joint International Accelerator School: Beam Loss and Accelerator Protection, Newport Beach, CA, USA , 5-14 Nov 201

Aeronautical engineering: A continuing bibliography with indexes (supplement 278)

This bibliography lists 414 reports, articles, and other documents introduced into the NASA scientific and technical information system in April 1992