16,732 research outputs found
Moving mesh finite difference solution of non-equilibrium radiation diffusion equations
A moving mesh finite difference method based on the moving mesh partial
differential equation is proposed for the numerical solution of the 2T model
for multi-material, non-equilibrium radiation diffusion equations. The model
involves nonlinear diffusion coefficients and its solutions stay positive for
all time when they are positive initially. Nonlinear diffusion and preservation
of solution positivity pose challenges in the numerical solution of the model.
A coefficient-freezing predictor-corrector method is used for nonlinear
diffusion while a cutoff strategy with a positive threshold is used to keep the
solutions positive. Furthermore, a two-level moving mesh strategy and a sparse
matrix solver are used to improve the efficiency of the computation. Numerical
results for a selection of examples of multi-material non-equilibrium radiation
diffusion show that the method is capable of capturing the profiles and local
structures of Marshak waves with adequate mesh concentration. The obtained
numerical solutions are in good agreement with those in the existing
literature. Comparison studies are also made between uniform and adaptive
moving meshes and between one-level and two-level moving meshes.Comment: 29 page
A Hybrid Godunov Method for Radiation Hydrodynamics
From a mathematical perspective, radiation hydrodynamics can be thought of as
a system of hyperbolic balance laws with dual multiscale behavior (multiscale
behavior associated with the hyperbolic wave speeds as well as multiscale
behavior associated with source term relaxation). With this outlook in mind,
this paper presents a hybrid Godunov method for one-dimensional radiation
hydrodynamics that is uniformly well behaved from the photon free streaming
(hyperbolic) limit through the weak equilibrium diffusion (parabolic) limit and
to the strong equilibrium diffusion (hyperbolic) limit. Moreover, one finds
that the technique preserves certain asymptotic limits. The method incorporates
a backward Euler upwinding scheme for the radiation energy density and flux as
well as a modified Godunov scheme for the material density, momentum density,
and energy density. The backward Euler upwinding scheme is first-order accurate
and uses an implicit HLLE flux function to temporally advance the radiation
components according to the material flow scale. The modified Godunov scheme is
second-order accurate and directly couples stiff source term effects to the
hyperbolic structure of the system of balance laws. This Godunov technique is
composed of a predictor step that is based on Duhamel's principle and a
corrector step that is based on Picard iteration. The Godunov scheme is
explicit on the material flow scale but is unsplit and fully couples matter and
radiation without invoking a diffusion-type approximation for radiation
hydrodynamics. This technique derives from earlier work by Miniati & Colella
2007. Numerical tests demonstrate that the method is stable, robust, and
accurate across various parameter regimes.Comment: accepted for publication in Journal of Computational Physics; 61
pages, 15 figures, 11 table
Modeling of Protostellar Clouds and their Observational Properties
A physical model and two-dimensional numerical method for computing the
evolution and spectra of protostellar clouds are described. The physical model
is based on a system of magneto-gasdynamical equations, including ohmic and
ambipolar diffusion, and a scheme for calculating the thermal and ionization
structure of a cloud. The dust and gas temperatures are determined during the
calculations of the thermal structure of the cloud. The results of computing
the dynamical and thermal structure of the cloud are used to model the
radiative transfer in continuum and in molecular lines. We presented the
results for clouds in hydrostatic and thermal equilibrium. The evolution of a
rotating magnetic protostellar cloud starting from a quasi-static state is also
considered. Spectral maps for optically thick lines of linear molecules are
analyzed. We have shown that the influence of the magnetic field and rotation
can lead to a redistribution of angular momentum in the cloud and the formation
of a characteristic rotational velocity structure. As a result, the
distribution of the velocity centroid of the molecular lines can acquire an
hourglass shape. We plan to use the developed program package together with a
model for the chemical evolution to interpret and model observed starless and
protostellar cores.Comment: Accepted to Astronomy Report
AREPO-RT: Radiation hydrodynamics on a moving mesh
We introduce AREPO-RT, a novel radiation hydrodynamic (RHD) solver for the
unstructured moving-mesh code AREPO. Our method solves the moment-based
radiative transfer equations using the M1 closure relation. We achieve second
order convergence by using a slope limited linear spatial extrapolation and a
first order time prediction step to obtain the values of the primitive
variables on both sides of the cell interface. A Harten-Lax-Van Leer flux
function, suitably modified for moving meshes, is then used to solve the
Riemann problem at the interface. The implementation is fully conservative and
compatible with the individual timestepping scheme of AREPO. It incorporates
atomic Hydrogen (H) and Helium (He) thermochemistry, which is used to couple
the ultra-violet (UV) radiation field to the gas. Additionally, infrared
radiation is coupled to the gas under the assumption of local thermodynamic
equilibrium between the gas and the dust. We successfully apply our code to a
large number of test problems, including applications such as the expansion of
regions, radiation pressure driven outflows and the levitation
of optically thick layer of gas by trapped IR radiation. The new implementation
is suitable for studying various important astrophysical phenomena, such as the
effect of radiative feedback in driving galactic scale outflows, radiation
driven dusty winds in high redshift quasars, or simulating the reionisation
history of the Universe in a self consistent manner.Comment: v2, accepted for publication in MNRAS, changed to a Strang split
scheme to achieve second order convergenc
A multigroup diffusion solver using pseudo transient continuation for a radiation-hydrodynamic code with patch-based AMR
We present a scheme to solve the nonlinear multigroup radiation diffusion
(MGD) equations. The method is incorporated into a massively parallel,
multidimensional, Eulerian radiation-hydrodynamic code with adaptive mesh
refinement (AMR). The patch-based AMR algorithm refines in both space and time
creating a hierarchy of levels, coarsest to finest. The physics modules are
time-advanced using operator splitting. On each level, separate level-solve
packages advance the modules. Our multigroup level-solve adapts an implicit
procedure which leads to a two-step iterative scheme that alternates between
elliptic solves for each group with intra-cell group coupling. For robustness,
we introduce pseudo transient continuation (PTC). We analyze the magnitude of
the PTC parameter to ensure positivity of the resulting linear system, diagonal
dominance and convergence of the two-step scheme. For AMR, a level defines a
subdomain for refinement. For diffusive processes such as MGD, the refined
level uses Dirichet boundary data at the coarse-fine interface and the data is
derived from the coarse level solution. After advancing on the fine level, an
additional procedure, the sync-solve (SS), is required in order to enforce
conservation. The MGD SS reduces to an elliptic solve on a combined grid for a
system of G equations, where G is the number of groups. We adapt the partial
temperature scheme for the SS; hence, we reuse the infrastructure developed for
scalar equations. Results are presented. (Abridged)Comment: 46 pages, 14 figures, accepted to JC
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