Related papers: Hyperbolic character of the angular moment equatio…
Radiative transfer and radiation hydrodynamics use the relativistic Boltzmann equation to describe the kinetics of photons. It is difficult to solve the six-dimensional time-dependent transfer equation unless the problem is highly symmetric…
In this paper we present an approach to approximate numerically the solution of coupled hyperbolic conservation laws. The coupling is achieved through a fixed interface, in which interface conditions are linking the traces of both sides.…
Godunov type numerical schemes for the class of hyperbolic systems, admitting non-classical $\delta-$ shocks are proposed. It is shown that the numerical approximations converge to the solution and preserve the physical properties of the…
General--relativistic, frequency--dependent radiative transfer in spherical, differentially--moving media is considered. In particular we investigate the character of the differential operator defined by the first two moment equations in…
Moment methods are classical approaches that approximate the mesoscopic radiative transfer equation by a system of macroscopic moment equations. An expansion in the angular variables transforms the original equation into a system of…
A number of physical phenomena are described by nonlinear hyperbolic equations. Presence of discontinuous solutions motivates the necessity of development of reliable numerical methods based on the fundamental mathematical properties of…
Statistical solutions are time-parameterized probability measures on spaces of integrable functions, that have been proposed recently as a framework for global solutions and uncertainty quantification for multi-dimensional hyperbolic system…
Stable numerical simulations for a hyperbolic system of conservation laws of relaxation type but not in divergence form are obtained by incorporating the physical entropy into the simulations. The entropy balance is utilized as an…
A direct numerical solution of the radiative transfer equation or any kinetic equation is typically expensive, since the radiative intensity depends on time, space and direction. An expansion in the direction variables yields an equivalent…
We present some analytical solutions to the Einstein equations, describing radiating collapsing spheres in the diffusion approximation. Solutions allow for modeling physical reasonable situations. The temperature is calculated for each…
Accurate accounting of particle number and 4-momentum in radiative transfer may be facilitated by the use of transport equations that allow transparent conversion between volume and surface integrals in both spacetime and momentum space.…
A higher order Godunov method for the radiation subsystem of radiation hydrodynamics is presented. A key ingredient of the method is the direct coupling of stiff source term effects to the hyperbolic structure of the system of conservation…
This article proposes a highly accurate and conservative method for hyperbolic systems using the finite volume approach. This innovative scheme constructs the intermediate states at the interfaces of the control volumes using the method of…
Linear models for the radiative transfer equation have been well developed, while nonlinear models are seldom investigated even for slab geometry due to some essential difficulties. We have proposed a moment model in MPN for slab geometry…
Observations and magnetohydrodynamic simulations of solar and stellar atmospheres reveal an intermittent behavior or steep gradients in physical parameters, such as magnetic field, temperature, and bulk velocities. The numerical solution of…
Hyperbolic conservation laws posed on manifolds arise in many applications to geophysical flows and general relativity. Recent work by the author and his collaborators attempts to set the foundations for a study of weak solutions defined on…
We consider multi-gradient fluids endowed with a volumetric internal energy which is a function of mass density, volumetric entropy and their successive gradients. We obtained the thermodynamic forms of equation of motions and equation of…
Continuum mechanics with dislocations, with the Cattaneo type heat conduction, with mass transfer, and with electromagnetic fields is put into the Hamiltonian form and into the form of the Godunov type system of the first order, symmetric…
A radiative transfer scheme is presented, based on a moment description of the equation of radiative transfer and the so-called ``M1 closure model'' for the Eddington tensor. This model features a strictly hyperbolic transport step for…
We investigate the spherically symmetric 1D ablation problem. We show that the parabolic heat equation fails to describe the approach to steady state in infinite space. The hyperbolic equation shows an approach to steady state with a time…