Hydrodynamic Shock Wave Studies within a Kinetic Monte Carlo Approach

Kinetic approaches are routinely employed to simulate the dynamics of systems that are too rarified to be described by the Navier-Stokes equations. However, generally they are far too computationally expensive to be applied for systems that are governed by continuum hydrodynamics. In this paper, we introduce a massively parallelized test-particle based kinetic Monte Carlo code that is capable of modeling the phase space evolution of an arbitrarily sized system that is free to move in and out of the continuum limit. Using particle mean free paths which are small with respect to the characteristic length scale of the simulated system, we retrieve continuum behavior, while non-equilibrium effects are observed when the mean free path is increased. To demonstrate the ability of our code to reproduce hydrodynamic solutions, we apply a test-suite of classic hydrodynamic shock problems. Simulations using tens of millions of test-particles are found to reproduce the analytical solutions well.Comment: 26 pages, 18 figures; corrections to text, new shock wave test adde

Building a Hydrodynamics Code with Kinetic Theory

We report on the development of a test-particle based kinetic Monte Carlo code for large systems and its application to simulate matter in the continuum regime. Our code combines advantages of the Direct Simulation Monte Carlo and the Point-of-Closest-Approach methods to solve the collision integral of the Boltzmann equation. With that, we achieve a high spatial accuracy in simulations while maintaining computational feasibility when applying a large number of test-particles. The hybrid setup of our approach allows us to study systems which move in and out of the hydrodynamic regime, with low and high particle densities. To demonstrate our code's ability to reproduce hydrodynamic behavior we perform shock wave simulations and focus here on the Sedov blast wave test. The blast wave problem describes the evolution of a spherical expanding shock front and is an important verification problem for codes which are applied in astrophysical simulation, especially for approaches which aim to study core-collapse supernovae.Comment: Proceedings for the Winter Workshop on Nuclear Dynamics 2013, 6 pages, 6 figure

Unified Gas-kinetic Wave-Particle Methods II: Multiscale Simulation on Unstructured Mesh

In this paper, we present a unified gas-kinetic wave-particle (UGKWP) method on unstructured mesh for multiscale simulation of continuum and rarefied flow. Inheriting from the multicale transport in the unified gas-kinetic scheme (UGKS), the integral solution of kinetic model equation is employed in the construction of UGKWP method to model the flow physics in the cell size and time step scales. A novel wave-particle adaptive formulation is introduced in the UGKWP method to describe the flow dynamics in each control volume. The local gas evolution is constructed through the dynamical interaction of the deterministic hydrodynamic wave and the stochastic kinetic particle. Within the resolution of cell size and time step, the decomposition, interaction, and evolution of the hydrodynamic wave and the kinetic particle depend on the ratio of the time step to the local particle collision time. In the rarefied flow regime, the flow physics is mainly recovered by the discrete particles and the UGKWP method performs as a stochastic particle method. In the continuum flow regime, the flow behavior is solely followed by macroscopic variable evolution and the UGKWP method becomes a gas-kinetic hydrodynamic flow solver for the viscous and heat-conducting Navier--Stokes solutions. In different flow regimes, many numerical test cases are computed to validate the UGKWP method on unstructured mesh. The UGKWP method can get the same UGKS solutions in all Knudsen regimes without the requirement of the time step and mesh size being less than than the particle collision time and mean free path. With an automatic wave-particle decomposition, the UGKWP method becomes very efficient. For example, at Mach number 30 and Knudsen number 0.1, in comparison with UGKS several-order-of-magnitude reductions in computational cost and memory requirement have been achieved by UGKWP

Light Curves from Supernova Shock Breakout through an Extended Wind

Recent observations suggest that some supernovae may be the result of an explosion into an optically thick circumstellar material, the product of pre-explosion mass-loss (wind) by the progenitor star. This scenario has been studied previously both analytically and numerically. However, many previous studies base their analysis on the diffusion approximation for radiation transfer, which is inappropriate in the optically thin outer layers of the wind. Here we study the deviations from diffusion, and calculate light curves more accurately using a Monte Carlo approach to photon transfer. We distinguish between "compact" winds, for which the diffusion approximation is appropriate, and "extended" winds, which require a more delicate treatment of the radiation. We show that this effect is more significant than that of the light travel time difference to a distant observer, which has a secondary influence on the light curves of extended-wind systems. We also comment on the applicability of the widely used flux-limited diffusion approximation in this context: we find that it generally does not reproduce the Monte Carlo results. The flux-limited diffusion approximation leads to results which are not only quantitatively, but also qualitatively wrong, in the extended-wind regime.Comment: Matched to published versio

Knudsen number dependence of 2D single-mode Rayleigh-Taylor fluid instabilities

We present a study of single-mode Rayleigh-Taylor instabilities (smRTI) with a modified Direct Simulation Monte Carlo (mDSMC) code in two dimensions. The mDSMC code is aimed to capture the dynamics of matter for a large range of Knudsen numbers within one approach. Our method combines the traditional Monte Carlo technique to efficiently propagate particles and the Point-of-Closest-Approach method for high spatial resolution. Simulations are performed using different particle mean-free-paths and we compare the results to linear theory predictions for the growth rate including diffusion and viscosity. We find good agreement between theoretical predictions and simulations and, at late times, observe the development of secondary instabilities, similar to hydrodynamic simulations and experiments. Large mean-free-paths favor particle diffusion, reduce the occurrence of secondary instabilities and approach the non-interacting gas limit.Comment: 15 pages, 12 figures, 1 tabl

Kinetic Simulations of Rayleigh-Taylor Instabilities

We report on an ongoing project to develop a large scale Direct Simulation Monte Carlo code. The code is primarily aimed towards applications in astrophysics such as simulations of core-collapse supernovae. It has been tested on shock wave phenomena in the continuum limit and for matter out of equilibrium. In the current work we focus on the study of fluid instabilities. Like shock waves these are routinely used as test-cases for hydrodynamic codes and are discussed to play an important role in the explosion mechanism of core-collapse supernovae. As a first test we study the evolution of a single-mode Rayleigh-Taylor instability at the interface of a light and a heavy fluid in the presence of a gravitational acceleration. To suppress small-wavelength instabilities caused by the irregularity in the separation layer we use a large particle mean free path. The latter leads to the development of a diffusion layer as particles propagate from one fluid into the other. For small amplitudes, when the instability is in the linear regime, we compare its position and shape to the analytic prediction. Despite the broadening of the fluid interface we see a good agreement with the analytic solution. At later times we observe the development of a mushroom like shape caused by secondary Kelvin-Helmholtz instabilities as seen in hydrodynamic simulations and consistent with experimental observations.Comment: Conference proceeding for The 30th Winter Workshop on Nuclear Dynamics 2014, 5 pages, 2 figure

Coupling of state-resolved rovibrational coarse-grain model for nitrogen to stochastic particle method for simulating internal energy excitation and dissociation

We propose to couple a state-resolved rovibrational coarse-grain model to a stochastic particle method for simulating internal energy excitation and dissociation of a molecular gas. An existing coarse-grain model based on the NASA Ames ab initio database for the N2-N system is modified using variably-spaced energy bins. Thermodynamic properties of the new coarse-grained model closely match those of the full set of rovibrational levels over a wide temperature range, using a number of bins much smaller than the complete mechanism. The chemical-kinetic behavior of the original equally -- and new variably -- spaced bin formulations is compared by simulating excitation and dissociation of N2 in an adiabatic, isochoric reactor. The variably-spaced formulation is better suited for reproducing the dynamics of the full database at conditions of interest in Earth reentry. Furthermore, we discuss details of our Direct Simulation Monte Carlo (DSMC) implementation for the coarse-grain model and describe changes to the collision algorithm necessary to accommodate our state-resolved reaction mechanism. The DSMC code is then verified against equivalent master equation (ME) calculations. In these simulations, state-resolved cross sections are used in analytical form. They verify micro-reversibility for the bins and allow for faster execution of the code. In our verification, we obtain very close agreement for the N and N2 concentrations, as well as the translational and rovibrational mode temperatures obtained independently using both methods. In addition to macroscopic moments, we compare internal energy populations predicted at selected time steps via DSMC and ME. We observe good agreement between both methods within the statistical scatter limits imposed by DSMC. In future work, the rovibrational coarse-grain model coupled to the particle method will allow us to study 3D reentry flow configurations.Comment: 40 pages, 19 figure

A MUSTA-FORCE algorithm for solving partial differential equations of relativistic hydrodynamics

Understanding event-by-event correlations and fluctuations is crucial for the comprehension of the dynamics of heavy ion collisions. Relativistic hydrodynamics is an elegant tool for modeling these phenomena; however, such simulations are time-consuming, and conventional CPU calculations are not suitable for event-by-event calculations. This work presents a feasibility study of a new hydrodynamic code that employs graphics processing units together with a general MUSTA-FORCE algorithm (Multi-Stage Riemann Algorithm - First Order Centered scheme) to deliver a high-performance yet universal tool for event-by-event hydrodynamic simulations. We also investigate the performance of selected slope limiters that reduce the amount of numeric oscillations and diffusion in the presence of strong discontinuities and shock waves. The numerical results are compared to the exact solutions to assess the code's accuracy.Comment: 22 pages, 10 figures, preprint draft to International Journal of Nonlinear Sciences and Numerical Simulatio

Ab initio simulation of warm dense matter

Warm dense matter (WDM) -- an exotic state of highly compressed matter -- has attracted high interest in recent years in astrophysics and for dense laboratory systems. At the same time, this state is extremely difficult to treat theoretically. This is due to the simultaneous appearance of quantum degeneracy, Coulomb correlations and thermal effects, as well as the overlap of plasma and condensed phases. Recent breakthroughs are due to the successful application of density functional theory (DFT) methods which, however, often lack the necessary accuracy and predictive capability for WDM applications. The situation has changed with the availability of the first \textit{ab initio} data for the exchange-correlation free energy of the warm dense uniform electron gas (UEG) that were obtained by quantum Monte Carlo (QMC) simulations, for recent reviews, see Dornheim \textit{et al.}, Phys. Plasmas \textbf{24}, 056303 (2017) and Phys. Rep. \textbf{744}, 1-86 (2018). In the present article we review recent further progress in QMC simulations of the warm dense UEG: namely, \textit{ab initio} results for the static local field correction $G(q)$ and for the dynamic structure factor $S(q,\omega)$. These data are of key relevance for the comparison with x-ray scattering experiments at free electron laser facilities and for the improvement of theoretical models. In the second part of this paper we discuss simulations of WDM out of equilibrium. The theoretical approaches include Born-Oppenheimer molecular dynamics, quantum kinetic theory, time-dependent DFT and hydrodynamics. Here we analyze strengths and limitations of these methods and argue that progress in WDM simulations will require a suitable combination of all methods. A particular role might be played by quantum hydrodynamics, and we concentrate on problems, recent progress, and possible improvements of this method

Particle acceleration and relativistic shocks

Observations of both gamma-ray burst sources and certain classes of active galaxy indicate the presence of relativistic shock waves and require the production of high energy particles to explain their emission. In this paper we review the basic theory of shock waves in relativistic hydrodynamics and magneto-hydrodynamics, emphasising the astrophysically interesting cases. This is followed by an overview of the theory of particle acceleration at such shocks. We summarise the applications to the astrophysics of relativistic jets and fireball models of gamma-ray-bursts.Comment: 43 pages, 5 figures, accepted for publication in Journal of Physics G: Nuclear and Particle Physics as a topical revie