CONVERGENCE RATE OF SOLUTIONS TO STRONG CONTACT DISCONTINUITY FOR THE ONE-DIMENSIONAL COMPRESSIBLE RADIATION HYDRODYNAMICS MODEL

This paper is concerned with a singular limit for the one-dimensional compress- ible radiation hydrodynamics model. The singular limit we consider corresponds to the physical problem of letting the Bouguer number infinite while keeping the Boltzmann number constant. In the case when the corresponding Euler system admits a contact discontinuity wave, Wang and Xie （2011） [12] recently verified this singular limit and proved that the solution of the compressible radiation hydrodynamics model converges to the strong contact 1 discontinuity wave in the L∞-norm away from the discontinuity line at a rate of ε1/4, as the reciprocal of the Bouguer number tends to zero. In this paper, Wang and Xie＇s convergence rate is improved to ε7/8 by introducing a new a priori assumption and some refined energy estimates. Moreover, it is shown that the radiation flux q tends to zero in the L∞-norm away from the discontinuity line, at a convergence rate as the reciprocal of the Bouguer number tends to zero.

ON LOCAL STRUCTURAL STABILITY OF ONE-DIMENSIONAL SHOCKS IN RADIATION HYDRODYNAMICS

In this paper, we are concerned with the local structural stability of one-dimensional shock waves in radiation hydrodynamics described by the isentropic Euler-Boltzmann equations. Even though in this radiation hydrodynamics model, the radiative effects can be understood as source terms to the isentropic Euler equations of hydrodynamics, in general the radiation field has singularities propagated in an angular domain issuing from the initial point across which the density is discontinuous. This is the major difficulty in the stability analysis of shocks. Under certain assumptions on the radiation parameters, we show there exists a local weak solution to the initial value problem of the one dimensional Euler-Boltzmann equations, in which the radiation intensity is continuous, while the density and velocity are piecewise Lipschitz continuous with a strong discontinuity representing the shock-front. The existence of such a solution indicates that shock waves are structurally stable, at least local in time, in radiation hydrodynamics.

Global Existence of Smooth Solutions for the Diffusion Approximation Model of General Gas in Radiation Hydrodynamics

In this paper,we consider the 3-D Cauchy problem for the diffusion approximation model in radiation hydrodynamics.The existence and uniqueness of global solutions is proved in perturbation framework,for more general gases including ideal poly tropic gas.Moreover,the optimal time decay rates are obtained for higher-order spatial derivatives of density,velocity,temperature,and radiation field.

A Colocalized Scheme for Three-Temperature Grey Diffusion Radiation Hydrodynamics

A positivity-preserving, conservative and entropic numerical scheme is presented for the three-temperature grey diffusion radiation hydrodynamics model. Moreprecisely, the dissipation matrices of the colocalized semi-Lagrangian scheme are de-fined in order to enforce the entropy production on each species (electron or ion) proportionally to its mass as prescribed in [34]. A reformulation of the model is then considered to enable the derivation of a robust convex combination based scheme. Thisyields the positivity-preserving property at each sub-iteration of the algorithm whilethe total energy conservation is reached at convergence. Numerous pure hydrodynamics and radiation hydrodynamics test cases are carried out to assess the accuracy of themethod. The question of the stability of the scheme is also addressed. It is observedthat the present numerical method is particularly robust.

Macroscopic lasereplasma interaction under strong non-local transport conditions for coupled matter and radiation

Reliable simulations of laseretarget interaction on the macroscopic scale are burdened by the fact that the energy transport is very often non-local.This means that the mean-free-path of the transported species is larger than the local gradient scale lengths and transport can be no longer considered diffusive.Kinetic simulations are not a feasible option due to tremendous computational demands,limited validity of the collisional operators and inaccurate treatment of thermal radiation.This is the point where hydrodynamic codes with non-local radiation and electron heat transport based on first principles emerge.The simulation code PETE(Plasma Euler and Transport Equations)combines both of them with a laser absorption method based on the Helmholtz equation and a radiation diffusion scheme presented in this article.In the case of modelling ablation processes it can be observed that both,thermal and radiative,transport processes are strongly non-local for laser intensities of 10^(13) W=cm^(2) and above.In this paper simulations for various laser intensities and different ablator materials are presented,where the non-local and diffusive treatments of radiation transport are compared.Significant discrepancies are observed,supporting importance of non-local transport for inertial confinement fusion related studies as well as for pre-pulse generated plasma in ultra-high intensity laseretarget interaction.

Generation of a sharp density increase in radiation transport between high-Z and low-Z plasmas

A sharp density increase(referred to as density incrustation)of the Au plasmas in the radiative cooling process of high-Z Au plasmas confined by low-Z CH plasmas is found through the radiative hydrodynamic simulations.The temperature of Au plasmas changes obviously in the cooling layer while the pressure remains constant.Consequently,the Au plasmas in the cooling layer are compressed,and the density incrustation is formed.It is also shown that when the high-Z plasma opacity decreases or the low-Z plasma opacity increases,the peak density of the density incrustation becomes lower and the thickness of the density incrustation becomes wider.This phenomenon is crucial to the Ray-leigheTaylor instability at the interface of high-Z and low-Z plasmas,since the density variation of Au plasmas has a considerable influence on the Atwood number of the interface.

Radiation Hydrodynamic Simulations in the Planar Scheme for the Fundamental Studies of Shock Ignition

As a fundamental and crucial research topic in the direct-driven inertial confinement fusion（ICF）,especially for shock ignition（SI）,investigation on the laser coupling with planar lowZ targets is beneficial for deep physical comprehension at the primary phase of SI.The production of the intense shock and the shock coalescence in the multi-layer targets,driven by the 3ω intense laser（351 nm the wavelength）,were studied in detail with the 1D and 2D radiation hydrodynamic simulations.It was inferred that the 1D simulation would overrate the shock velocity and the ablation pressure of the spike;the coalescence time and the velocity of the coalescence shock depended evidently on the pulse shape and the start time of the spike.The present study can also provide a semi-quantitative reference for the design of the SI decomposition experiments on the Shenguang-III prototype laser facility.

Early afterglows from radially structured outflows and the application to X-ray shallow decays

In the fireball model, it is more physically realistic that ganuna-ray burst （GRB） ejecta have a range of bulk Lorentz factors （assuming M ∝ Г^-8）. The low Lorentz factor part of the ejecta will catch up with the high Lorentz factor part when the latter is decelerated by the surrounding medium to a comparable Lorentz factor. Such a process will develop a long-lasting weak reverse shock until the whole ejecta are shocked. Meanwhile, the forward shocked materials are gradually supplied with energy from the ejecta that are catching-up, and thus the temporal decay of the forward shock emission will be slower than that without an energy supply. However, the reverse shock may be strong. Here, we extend the standard reverse-forward shock model to the case of radially nonuniform ejecta. We show that this process can be classified into two cases： the thick shell case and the thin shell case. In the thin shell case, the reverse shock is weak and the temporal scaling law of the afterglow is the same as that in Sad ＆ Meszaros （2000）. However, in the thick shell case, the reverse shock is strong and thus its emission dominates the afterglow in the high energy band. Our results also show slower decaying behavior of the afterglow due to the energy supply by low Lorentz factor materials, which may help the understanding of the plateau observed in the early optical and X-ray afterglows.

On the Light Curves of GRB Afterglows

We present gamma-ray burst afterglow light curves in X-ray, optical and radio bands for various distributions of accelerated electrons behind the shock. The effects of lateral expansion of the jet and of winds in typical Wolf-Rayet star on the evolution are discussed. The light curves in the radiative case decline more rapidly than those in the adiabatic case. Under the combined effect of jet expansion and wind environment, the light curves have the greatest deviation from those of the standard model. All these results refer to the relativistic phase.

αSetup-PCTL:An Adaptive Setup-Based Two-Level Preconditioner for Sequence of Linear Systems of Three-Temperature Energy Equations

The iterative solution of the sequence of linear systems arising from threetemperature(3-T)energy equations is an essential component in the numerical simulation of radiative hydrodynamic(RHD)problem.However,due to the complicated application features of the RHD problems,solving 3-T linear systems with classical preconditioned iterative techniques is challenging.To address this difficulty,a physicalvariable based coarsening two-level(PCTL)preconditioner has been proposed by dividing the fully coupled system into four individual easier-to-solve subsystems.Despite its nearly optimal complexity and robustness,the PCTL algorithm suffers from poor efficiency because of the overhead associatedwith the construction of setup phase and the solution of subsystems.Furthermore,the PCTL algorithm employs a fixed strategy for solving the sequence of 3-T linear systems,which completely ignores the dynamically and slowly changing features of these linear systems.To address these problems and to efficiently solve the sequence of 3-T linear systems,we propose an adaptive two-level preconditioner based on the PCTL algorithm,referred to as αSetup-PCTL.The adaptive strategies of the αSetup-PCTL algorithm are inspired by those of αSetup-AMG algorithm,which is an adaptive-setup-based AMG solver for sequence of sparse linear systems.The proposed αSetup-PCTL algorithm could adaptively employ the appropriate strategies for each linear system,and thus increase the overall efficiency.Numerical results demonstrate that,for 36 linear systems,the αSetup-PCTL algorithm achieves an average speedup of 2.2,and a maximum speedup of 4.2 when compared to the PCTL algorithm.

On Arbitrary-Lagrangian-Eulerian One-Step WENO Schemes for Stiff Hyperbolic Balance Laws

In this article we present a new family of high order accurate Arbitrary Lagrangian-Eulerian one-step WENO finite volume schemes for the solution of stiff hyperbolic balance laws.High order accuracy in space is obtained with a standard WENO reconstruction algorithm and high order in time is obtained using the local space-time discontinuous Galerkinmethod recently proposed in[20].In the Lagrangian framework considered here,the local space-time DG predictor is based on a weak formulation of the governing PDE on a moving space-time element.For the spacetime basis and test functions we use Lagrange interpolation polynomials defined by tensor-product Gauss-Legendre quadrature points.The moving space-time elements are mapped to a reference element using an isoparametric approach,i.e.the spacetime mapping is defined by the same basis functions as the weak solution of the PDE.We show some computational examples in one space-dimension for non-stiff and for stiff balance laws,in particular for the Euler equations of compressible gas dynamics,for the resistive relativistic MHD equations,and for the relativistic radiation hydrodynamics equations.Numerical convergence results are presented for the stiff case up to sixth order of accuracy in space and time and for the non-stiff case up to eighth order of accuracy in space and time.