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Register a new userA radiation-hydrodynamics scheme valid from the transport to the diffusion limit
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We present in this paper the numerical treatment of the coupling between hydrodynamics and radiative transfer. The fluid is modeled by classical conservation laws (mass, momentum and energy) and the radiation by the grey moment $M_1$ system. The scheme introduced is able to compute accurate numerical solution over a broad class of regimes from the transport to the diffusive limits. We propose an asymptotic preserving modification of the HLLE scheme in order to treat correctly the diffusion limit. Several numerical results are presented, which show that this approach is robust and have the correct behavior in both the diffusive and free-streaming limits. In the last numerical example we test this approach on a complex physical case by considering the collapse of a gas cloud leading to a proto-stellar structure which, among other features, exhibits very steep opacity gradients.
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The paper proposes a second-order accurate direct Eulerian generalized Riemann problem (GRP) scheme for the radiation hydrodynamical equations (RHE) in the zero diffusion limit. The difficulty comes from no explicit expression of the flux in terms of the conservative vector. The characteristic fields and the relations between the left and right states across the elementary-waves are first studied, and then the solution of the one-dimensional Riemann problem is analyzed and given. Based on those, the direct Eulerian GRP scheme is derived by directly using the generalized Riemann invariants and the Runkine-Hugoniot jump conditions to analytically resolve the left and right nonlinear waves of the local GRP in the Eulerian formulation. Several numerical examples show that the GRP scheme can achieve second-order accuracy and high resolution of strong discontinuity.
We analyze the evolution of hydrodynamic fluctuations for QCD matter below $T_c$ in the chiral limit, where the pions (the Goldstone modes) must be treated as additional non-abelian superfluid degrees of freedom, reflecting the broken $SU_L(2) times SU_R(2)$ symmetry of the theory. In the presence of a finite pion mass $m_{pi}$, the hydrodynamic theory is ordinary hydrodynamics at long distances, and superfluid-like at short distances. The presence of the superfluid degrees of freedom then gives specific contributions to the bulk viscosity, the shear viscosity, and diffusion coefficients of the ordinary theory at long distances which we compute. This determines, in some cases, the leading dependence of the transport parameters of QCD on the pion mass. We analyze the predictions of this computation, as the system approaches the $O(4)$ critical point.
The radiation magnetohydrodynamics (RMHD) system couples the ideal magnetohydrodynamics equations with a gray radiation transfer equation. The main challenge is that the radiation travels at the speed of light while the magnetohydrodynamics changes with the time scale of the fluid. The time scales of these two processes can vary dramatically. In order to use mesh sizes and time steps that are independent of the speed of light, asymptotic preserving (AP) schemes in both space and time are desired. In this paper, we develop an AP scheme in both space and time for the RMHD system. Two different scalings are considered. One results in an equilibrium diffusion limit system, while the other results in a non-equilibrium system. The main idea is to decompose the radiative intensity into three parts, each part is treated differently with suitable combinations of explicit and implicit discretizations guaranteeing the favorable stability conditionand computational efficiency. The performance of the AP method is presented, for both optically thin and thick regions, as well as for the radiative shock problem.
We present an analysis of the general relativistic Boltzmann equation for radiation, appropriate to the case where particles and photons interact through Thomson scattering, and derive the radiation energy-momentum tensor in the diffusion limit, with viscous terms included. Contrary to relativistic generalizations of the viscous stress tensor that appear in the literature, we find that the stress tensor should contain a correction to the comoving energy density proportional to the divergence of the four-velocity, as well as a finite bulk viscosity. These modifications are consistent with the framework of radiation hydrodynamics in the limit of large optical depth, and do not depend on thermodynamic arguments such as the assignment of a temperature to the zeroth-order photon distribution. We perform a perturbation analysis on our equations and demonstrate that, as long as the wave numbers do not probe scales smaller than the mean free path of the radiation, the viscosity contributes only decaying, i.e., stable, corrections to the dispersion relations. The astrophysical applications of our equations, including jets launched from super-Eddington tidal disruption events and those from collapsars, are discussed and will be considered further in future papers.
Radiation controls the dynamics and energetics of many astrophysical environments. To capture the coupling between the radiation and matter, however, is often a physically complex and computationally expensive endeavour. We develop a numerical tool to perform radiation-hydrodynamics simulations in various configurations at an affordable cost. We build upon the finite volume code MPI-AMRVAC to solve the equations of hydrodynamics on multi-dimensional adaptive meshes and introduce a new module to handle the coupling with radiation. A non-equilibrium, flux-limiting diffusion approximation is used to close the radiation momentum and energy equations. The time-dependent radiation energy equation is then solved within a flexible framework, accounting fully for radiation forces and work terms and further allowing the user to adopt a variety of descriptions for the radiation-matter interaction terms (the opacities). We validate the radiation module on a set of standard testcases for which different terms of the radiative energy equation predominate. As a preliminary application to a scientific case, we calculate spherically symmetric models of the radiation-driven and optically thick supersonic outflows from massive Wolf-Rayet stars. This also demonstrates our codes flexibility, as the illustrated simulation combines opacities typically used in static stellar structure models with a parametrised form for the enhanced line-opacity expected in supersonic flows. This new module provides a convenient and versatile tool to perform multi-dimensional and high resolution radiative-hydrodynamics simulations in optically thick environments with the MPI-AMRVAC code. The code is ready to be used for a variety of astrophysical applications, where a first target for us will be multi-dimensional simulations of stellar outflows from Wolf-Rayet stars.
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