Equations Of Radiation Hydrodynamics Research Articles

RHDLPP: A multigroup radiation hydrodynamics code for laser-produced plasmas

In this paper, we introduce the RHDLPP, a flux-limited multigroup radiation hydrodynamics numerical code designed for simulating laser-produced plasmas in diverse environments. The code bifurcates into two packages: RHDLPP-LTP for low-temperature plasmas generated by moderate-intensity nanosecond lasers, and RHDLPP-HTP for high-temperature, high-density plasmas formed by high-intensity laser pulses. The core radiation hydrodynamic equations are resolved in the Eulerian frame, employing an operator-split method. This method decomposes the solution into two substeps: first, the explicit resolution of the hyperbolic subsystems integrating radiation and fluid dynamics; second, the implicit treatment of the parabolic part comprising stiff radiation diffusion, heat conduction, and energy exchange. Laser propagation and energy deposition are modeled through a hybrid approach, combining geometrical-optics ray-tracing in sub-critical plasma regions with a one-dimensional solution of the Helmholtz wave equation in super-critical areas. The thermodynamic states are ascertained using an equation of state, based on either the real gas approximation or the quotidian equation of state (QEOS). For ionization calculations, the code employs a steady-state collisional-radiation (CR) model using the screened-hydrogenic approximation. Additionally, RHDLPP includes RHDLPP-SpeIma3D, a three-dimensional spectral simulation post-processing module, for generating both temporally-spatially resolved and time-integrated spectra and imaging, facilitating direct comparisons with experimental data. The paper showcases a series of verification tests to establish the code's accuracy and efficiency, followed by application cases, including simulations of laser-produced aluminium (Al) plasmas, pre-pulse-induced target deformation of tin (Sn) microdroplets relevant to extreme ultraviolet lithography light sources, and varied imaging and spectroscopic simulations. These simulations highlight RHDLPP's effectiveness and applicability in fields such as laser-induced breakdown spectroscopy, extreme ultraviolet lithography sources, and high-energy-density physics.

Bridging the Gap between Luminous Red Novae and Common Envelope Evolution: The Role of Recombination Energy and Radiation Force

Luminous red novae and their connection to common envelope evolution (CEE) remain elusive in astrophysics. Here, we present a radiation hydrodynamic model capable of simulating the light curves of material ejected during a CEE. For the first time, the radiation hydrodynamic model incorporates complete recombination physics for hydrogen and helium. The radiation hydrodynamic equations are solved with Guangqi. With time-independent ejecta simulations, we show that the peaks in the light curves are attributed to radiation-dominated ejecta, while the extended plateaus are produced by matter-dominated ejecta. To showcase our model’s capability, we fit the light curve of AT 2019zhd. The central mass object of 6 M ⊙ is assumed based on observations and scaling relations. Our model demonstrates that the ejecta mass of AT 2019zhd falls within the range of 0.04–0.1 M ⊙. Additionally, we demonstrate that recombination energy and radiation force acceleration significantly impact the light curves, whereas dust formation has a limited effect during the peak and plateau phases.

Hydrodynamic models of pulsation period evolution in R Hydrae

ABSTRACT Pulsation period evolution during the helium–shell flash in the Mira variable R Hya is investigated using consistent stellar evolution and non-linear stellar pulsation computations. The initial and time-dependent inner boundary conditions for the equations of radiation hydrodynamics describing non-linear stellar oscillations were determined using a grid of TP–AGB model sequences with initial masses on the main sequence 1.5M⊙ ≤ MZAMS ≤ 5.0M⊙ and the initial metallicity Z = 0.014. The setup of initial conditions for hydrodynamic models corresponds to ≈100 yr prior to the maximum of the helium–shell luminosity and ensures that the stellar envelope of the evolution model is under both hydrostatic and thermal equilibrium. Solution of the equations of hydrodynamics allowed us to determine the temporal variation of the pulsation period Π(t) during ≈500 yr. Within this time interval R Hya is a fundamental mode pulsator. The period temporal dependencies Π(t) calculated for the AGB star models at the beginning of the third dredge-up phase and with masses $4.4M_{\odot }\lessapprox M\lessapprox 4.5M_{\odot }$ are in agreement with observational estimates of the period of R Hya obtained during last two centuries. The mean radius of R Hya pulsation models at the end of the XX century ($470 R_{\odot }\lessapprox \bar{R}\lessapprox 490 R_{\odot }$) agrees with observational estimates obtained using the interferometric angular diameter measurements.

High order conservative Lagrangian schemes for two-dimensional radiation hydrodynamics equations in the equilibrium-diffusion limit

Radiation hydrodynamics equations (RHE) refer to the study of how interactions between radiation and matter influence thermodynamic states and dynamic flow, which has been widely applied to high temperature hydrodynamics, such as inertial confinement fusion (ICF) and astrophysical gaseous stars. Solving RHE accurately and robustly even under the equilibrium diffusion approximation is a challenging task. To address this, we develop two types of high order conservative Lagrangian schemes for RHE in the equilibrium-diffusion limit for the two dimensional case on the Lagrangian moving mesh. Based on the multi-resolution WENO reconstruction for the spatial discretization and strong stability preserving Runge-Kutta (SSP-RK) time discretization, we first develop an explicit Lagrangian scheme with the HLLC numerical flux to achieve high order accuracy in space and time. We also discuss the positivity-preserving property of the high order explicit Lagrangian scheme. To overcome the severe time step restriction arising from the nonlinear radiation diffusion term in the explicit scheme, we further present a high order explicit-implicit-null (EIN) Lagrangian scheme. By adding a sufficiently large linear diffusion term on both sides of the scheme, we treat the complicated nonlinear parts explicitly and efficiently, and treat the added linear diffusion term on the right-hand side implicitly with a relaxed time step restriction. According to our numerical experiments, these two types of Lagrangian schemes are high order accurate, conservative and can capture the interfaces automatically. Additionally, the explicit scheme is found to be non-oscillatory and can preserve positivity while maintaining the original high order accuracy.

High order conservative Lagrangian scheme for three-temperature radiation hydrodynamics

The three-temperature (3-T) radiation hydrodynamics (RH) equations are widely used in modeling various optically thick high-energy-density-physics environments, such as those in astrophysics and inertial confinement fusion (ICF). In this paper, we will discuss the methodology to construct a high order conservative Lagrangian scheme solving 3-T RH equations. Specifically, the three new energy variables are defined first, in the form of which the three energy equations of the 3-T RH equations are rewritten. The main advantage of this formulation is that it facilitates the design of a scheme with both conservative property and arbitrary high order accuracy. Starting from one dimension and based on the multi-resolution WENO reconstruction and the strong stability preserving (SSP) high order time discretizations, taken as an example, we design a third order conservative Lagrangian scheme both in space and time. To determine the numerical flux for the conservative advection terms in the 3-T RH equations, we propose a HLLC numerical flux which is derived from the divergence theorem rigorously and is suitable for multi-material problems with the ideal-gas equations of state. After that, we discuss how to design a class of high order positivity-preserving explicit Lagrangian schemes to solve the 3-T RH equations which only contain the conservative advection terms in space. Preliminary extension to the two dimensional case is also considered. Finally, various numerical tests are given to verify the desired properties of the high order Lagrangian schemes such as high order accuracy, non-oscillation, conservation and adaptation to multi-material problems.

Blowup and non-global existence of smooth solutions to the one-dimensional Euler–Boltzmann equations

In this paper, we study the blowup and non-global existence of smooth solutions to the one-dimensional Euler–Boltzmann equations of radiation hydrodynamics. First, we improve the blowup result in [P. Jiang and Y. G. Wang, Initial-boundary value problems and formation of singularities for one-dimensional non-relativistic radiation hydrodynamic equations, J. Hyperbolic Differential Equations 9 (2012) 711–738] on the half line [Formula: see text] for large initial data by removing a restrict condition. Next, we obtain a new blowup result on the half line [Formula: see text] by introducing a new momentum weight. Finally, we present two non-global existence results for the smooth solutions to the one-dimensional Euler–Boltzmann equations with vacuum on the interval [Formula: see text] by introducing some new average quantities.

The Nature of Anomalous Period Increase in the Pulsating Variable V725 Sgr

The evolutionary tracks of stars with masses on the main sequence $$0.84\;M_{\odot}\leq M_{\textrm{ZAMS}}\leq 0.95\;M_{\odot}$$ and initial metal abundances $$Z=0.006$$ and $$0.01$$ were computed under various assumptions about the mass loss rate at the red giant stage as well as at the AGB and the post-AGB stages. Among 160 evolutionary sequences we selected nearly 30 sequences where the final thermal flash of the helium shell source occurs in the early post-AGB stage when the ratio of the hydrogen envelope mass to the stellar mass ranges from 0.01 to 0.08. Selected evolutionary sequences were used for calculation of initial and inner boundary conditions used in solution of the equations of radiation hydrodynamics and turbulent convection describing evolution of stellar pulsations after the helium flash. Among about three dozen hydrodynamic models we found the three ones demonstrating almost eightfold increase of the pulsation period observed in V725 Sgr during the last century as well as the gradual transformation of fairly regular pulsations with period $$\Pi\approx 12$$ day to semi–regular non-linear oscillations with period $$80\lesssim\Pi\lesssim 90\text{ day}$$ . We conclude that the anomalous growth of the pulsation period in V725 Sgr is due to the final thermal flash of the helium shell source that occurred in the early post-AGB star with mass $$M\approx 0.53\;M_{\odot}$$ and the mass of the hydrogen envelope ranging from $$0.013$$ to $$0.019\;M_{\odot}$$ .

On regular solutions to compressible radiation hydrodynamic equations with far field vacuum

Abstract The Cauchy problem for three-dimensional (3D) isentropic compressible radiation hydrodynamic equations is considered. When both shear and bulk viscosity coefficients depend on the mass density ρ \rho in a power law ρ δ {\rho }^{\delta } (with 0 < δ < 1 0\lt \delta \lt 1 ), based on some elaborate analysis of this system’s intrinsic singular structures, we establish the local-in-time well-posedness of regular solution with arbitrarily large initial data and far field vacuum in some inhomogeneous Sobolev spaces by introducing some new variables and initial compatibility conditions. Note that due to the appearance of the vacuum, the momentum equations are degenerate both in the time evolution and viscous stress tensor, which, along with the strong coupling between the fluid and the radiation field, make the study on corresponding well-posedness challenging. For proving the existence, we first introduce an enlarged reformulated structure by considering some new variables, which can transfer the degeneracies of the radiation hydrodynamic equations to the possible singularities of some special source terms, and then carry out some singularly weighted energy estimates carefully designed for this reformulated system.

Thermal Instability in Radiation Hydrodynamics: Instability Mechanisms, Position-dependent S-curves, and Attenuation Curves

Local thermal instability can plausibly explain the formation of multiphase gas in many different astrophysical environments, but the theory of local TI is only well-understood in the optically thin limit of the equations of radiation hydrodynamics (RHD). Here, we lay groundwork for transitioning from this limit to a full RHD treatment assuming a gray opacity formalism. We consider a situation where the gas becomes thermally unstable due to the hardening of the radiation field when the main radiative processes are free–free cooling and Compton heating. We identify two ways in which this can happen: (i) when the Compton temperature increases with time, through a rise in either the intensity or energy of a hard X-ray component; and (ii) when attenuation reduces the flux of the thermal component such that the Compton temperature increases with depth through the slab. Both ways likely occur in the broad-line region of active galactic nuclei where columns of gas can be ionization-bounded. In such instances where attenuation is significant, thermal equilibrium solution curves become position-dependent and it no longer suffices to assess the stability of an irradiated column of gas at all depths using a single equilibrium curve. We demonstrate how to analyze a new equilibrium curve—the attenuation curve—for this purpose, and we show that, by Field’s instability criterion, a negative slope along this curve indicates that constant-density slabs are thermally unstable whenever the gas temperature increases with depth.

General Relativistic Implicit Monte Carlo Radiation-hydrodynamics

We report on a new capability added to our general relativistic radiation-magnetohydrodynamics code, Cosmos++: an implicit Monte Carlo (IMC) treatment for radiation transport. The method is based on a Fleck-type implicit discretization of the radiation-hydrodynamics equations, but generalized for both Newtonian and relativistic regimes. A multiple reference frame approach is used to geodesically transport photon packets (and solve the hydrodynamics equations) in the coordinate frame, while radiation–matter interactions are handled either in the fluid or electron frames then communicated via Lorentz boosts and orthonormal tetrad bases attached to the fluid. We describe a method for constructing estimators of radiation moments using path-weighting that generalizes to arbitrary coordinate systems in flat or curved spacetime. Absorption, emission, scattering, and relativistic Comptonization are among the matter interactions considered in this report. We discuss our formulations and numerical methods, and validate our models against a suite of radiation and coupled radiation-hydrodynamics test problems in both flat and curved spacetimes.

VETTAM: a scheme for radiation hydrodynamics with adaptive mesh refinement using the variable Eddington tensor method

ABSTRACT We present Variable Eddington Tensor (VET)-closed Transport on Adaptive Meshes (VETTAM), a new algorithm to solve the equations of radiation hydrodynamics (RHD) with support for adaptive mesh refinement (AMR) in a frequency-integrated, two-moment formulation. The method is based on a non-local VET closure computed with a hybrid characteristics scheme for ray tracing. We use a Godunov method for the hyperbolic transport of radiation with an implicit backwards-Euler temporal update to avoid the explicit time-step constraint imposed by the light-crossing time, and a fixed-point Picard iteration scheme to handle the nonlinear gas-radiation exchange term, with the two implicit update stages jointly iterated to convergence. We also develop a modified wave-speed correction method for AMR, which we find to be crucial for obtaining accurate results in the diffusion regime. We demonstrate the robustness of our scheme with a suite of pure radiation and RHD tests, and show that it successfully captures the streaming, static diffusion, and dynamic diffusion regimes and the spatial transitions between them, casts sharp shadows, and yields accurate results for rates of momentum and energy exchange between radiation and gas. A comparison between different closures for the radiation moment equations, with the Eddington approximation (0th-moment closure) and the M1 approximation (1st-moment closure), demonstrates the advantages of the VET method (2nd-moment closure) over the simpler closure schemes. VETTAM has been coupled to the AMR FLASH (magneto-)hydrodynamics code and we summarize by reporting performance features and bottlenecks of our implementation.

Determination of the symmetry groups of radiation hydrodynamics equations and the compatible equations of state and opacities

The purpose of this study was to find all the symmetry groups of the radiation hydrodynamics equations with no a priori assumptions on the equations of state (EOS) and opacities. As shown in earlier works, the application of the Lie group technique to such a system of equations leads to invariance conditions in the form of linear differential equations, which, up until now, were only partially solved. In this paper, using the same technique and under the same assumptions, but with a simpler formulation, we show that these equations can be entirely solved analytically. This result enables us to list all the one-parameter groups that may be symmetry groups of the system. To be actually so, they must be associated with suitable EOS and opacities whose general expressions are also given. The interesting point is that some of them can be chosen so as to fit realistic data for EOS and opacities. Using this property, we propose a method to design low-scale experiments to simulate radiative processes, which would involve too much energy to have experimented with at their full scale. In addition, we derive the reduced systems associated with the one-parameter symmetry groups found. We show that some classical self-similar problems can be extended to more general EOS and opacities, and we treat in detail the self-similar expansion of a semi-infinite medium submitted to an internal source of energy.

An operator splitting method for solving dimensionless radiation hydrodynamics equations

By non-dimensionalizing the radiation hydrodynamics equations in the form of Boltzmann-Euler coupling, the two moments approximate model written with non-dimensional variables is proposed and the non-dimensionalization leads to two parameters. An operator splitting method is developed to solve the dimensionless radiation hydrodynamics equations. The advantage of this method is that instead of solving nonlinear equations, it solves a set of ordinary differential equations, and these ordinary differential equations are decoupled. Lastly, the paper describes the Su-Olson problem which has a semi-analytic solution. The analysis shows that the solutions of numerical simulation agree well with the semi-analytic solutions in equilibrium diffusion limit.

A variable Eddington factor method with different spatial discretizations for the radiative transfer equation and the hydrodynamics/radiation-moment equations

The purpose of this paper is to present a High-Order/Low-Order radiation-hydrodynamics method that is second-order accurate in both space and time and uses the Variable Eddington Factor (VEF) method to couple a high-order set of 1-D slab-geometry grey Sn radiation transport equations with a low-order set of radiation moment and hydrodynamics equations. The Sn equations are spatially discretized with a lumped linear-discontinuous Galerkin scheme, while the low-order radiation-hydrodynamics equations are spatially discretized with a constant-linear mixed finite-element scheme. Both the high-order and low-order equations are discretized in time using a trapezoidal BDF-2 method. One manufactured solution is used to demonstrate that the scheme is second-order accurate for smooth solutions, and another one is used to demonstrate that the scheme is asymptotic-preserving in the equilibrium-diffusion limit. Calculations are performed for radiative shock problems and compared with semi-analytic solutions. In a previous paper it was shown that the pure radiative transfer scheme (the Sn equations coupled to the radiation moment equations and a material temperature equation rather than the hydrodynamics equations) is asymptotic-preserving in the equilibrium-diffusion limit, is well-behaved with unresolved spatial boundary layers in that limit, and yields accurate Marshak wave speeds even with strongly temperature-dependent opacities and relatively coarse meshes. These same properties carry over to our radiation-hydrodynamics scheme.

Algorithm of radiation hydrodynamics with nonorthogonal mesh for 3D implosion problem

It is crucial to understand the degradation of implosion performance caused by three-dimensional physics and the implementation of 3-D spherical mesh is challenging. In this paper a mesh generation method based on the cube spherical projection is proposed for 3D implosion problem in Inertial Confinement Fusion (ICF). This kind of mesh has the advantage of good quality, convenient adding radiation source and adaptive moving in the radial direction. Together, a mathematical model of radiation hydrodynamics with ion-electron non-equilibrium is present. The equations of radiation hydrodynamics are solved with the operator splitting method, such that the hydrodynamics equations are solved explicitly making use of the capability of well understood explicit schemes while the radiation diffusion and electron/ion conduction parts are solved implicitly by an eleven-point scheme on the non-orthogonal mesh. We present results from several benchmark problems in order to validate our numerical scheme. And finally, we investigate the development of fourth-order modes and compute the disturbance growth process of hot spot boundary, which shown that it conforms to the physical law.

Numerical Simulation of Sub-Terahertz Thermal Emission: RADYN Code

The temporal evolution of thermal bremsstrahlung in the sub-terahertz range is calculated for F-CHROMA models of the flare chromosphere and transition region ( https://www.fchroma.org ). These models are calculated based on the numerical solution of the system of equations of radiation hydrodynamics with the RADYN code, which describes the response of chromospheric plasma to the flux of accelerated electrons in the form of a triangular pulse. It is found that the positive slope of the spectrum in the frequency range of 93–400 GHz is formed during the entire burst. The sub-THz radiation peak can be both ahead and behind the maximum of the function of the injection of energetic electrons depending on the number and index of the spectrum of precipitating particles. In some cases, the time profile of the sub-THz radiation is quite complex and pulsating due to gas-dynamic phenomena in the chromosphere and transition region.

Local well‐posedness of compressible radiation hydrodynamic equations with density‐dependent viscosities and vacuum

In this paper, we consider the Cauchy problem for three‐dimensional isentropic compressible radiation hydrodynamic equations with density‐dependent viscosity coefficients. When the viscosity coefficients are given as power of density (ρδ with δ > 1), we establish the local‐in‐time existence of classical solutions containing a vacuum for large initial data. Here, we point out that the initial layer compatibility conditions are not necessary.

Efficient smoothed particle radiation hydrodynamics II: Radiation hydrodynamics

The radiation hydrodynamics equations for smoothed particle hydrodynamics are derived by operator splitting the radiation and hydrodynamics terms, including necessary terms for material motion, and discretizing each of the sets of equations separately in time and space. The implicit radiative transfer discussed in the first paper of this series is coupled to explicit smoothed particle hydrodynamics. The result is a multi-material meshless radiation hydrodynamics code with arbitrary opacities and equations of state that performs well for problems with significant material motion. The code converges with second-order accuracy in space and first-order accuracy in time to the semianalytic solution for the Lowrie radiative shock problem and has competitive performance compared to a mesh-based radiation hydrodynamics code for a multi-material problem in two dimensions and an ablation problem inspired by inertial confinement fusion in two and three dimensions.

Relativistic radiation hydrodynamics in a reference-metric formulation

We adopt a two-moment formalism, together with a reference-metric approach, to express the equations of relativistic radiation hydrodynamics in a form that is well-suited for numerical implementations in curvilinear coordinates. We illustrate the approach by employing a gray opacity in an optically thick medium. As numerical demonstrations we present results for two test problems, namely stationary, slab-symmetric solutions in flat spacetimes, including shocks, and heated Oppenheimer-Snyder collapse to a black hole. For the latter, we carefully analyze the transition from an initial transient to a post-transient phase that is well described by an analytically-known diffusion solution. We discuss the properties of the numerical solution when rendered in moving-puncture coordinates.

Mass transfer in AGB binaries - uncovering a new evolution channel by 3D radiation-hydrodynamic simulations

AbstractThe origin of chemically peculiar stars and nonzero eccentricity in evolved close binaries have been long-standing problems in binary stellar evolution. Answers to these questions may trace back to an intense mass transfer during the asymptotic-giant-branch (AGB) binary phase. We use AstroBEAR to solve the 3D radiation hydrodynamic equations and calculate the mass transfer rate in AGB binaries that undergo the wind-Roche-lobe overflow or Bondi-Hoyle-Lyttleton (BHL) accretion. One of the goals of this work is to illustrate the transition from the wind- Roche-lobe overflow to BHL accretion. Both circumbinary disks and spiral structure outflows can appear in the simulations. As a result of enhanced mass transfer and angular momentum transfer, some AGB binaries may undergo orbit shrinkage, and some will expand. The high mass transfer efficiency is closely related to the presence of the circumbinary disks.