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New mathematical and numerical results are given for the coupling of the temperature equation of a fluid with Radiative Transfer: existence and uniqueness and a convergent monotone numerical scheme. The technique is shown to be feasible for studying the temperature of lake Leman heated by the sun and for the earth atmosphere to study the effects of greenhouse gases.
Linear kinetic transport equations play a critical role in optical tomography, radiative transfer and neutron transport. The fundamental difficulty hampering their efficient and accurate numerical resolution lies in the high dimensionality of the phy
We propose a new approach to the numerical solution of radiative transfer equations with certified a posteriori error bounds. A key role is played by stable Petrov--Galerkin type variational formulations of parametric transport equations and correspo
In this paper, we will develop a class of high order asymptotic preserving (AP) discontinuous Galerkin (DG) methods for nonlinear time-dependent gray radiative transfer equations (GRTEs). Inspired by the work cite{Peng2020stability}, in which stabili
Science and engineering problems subject to uncertainty are frequently both computationally expensive and feature nonsmooth parameter dependence, making standard Monte Carlo too slow, and excluding efficient use of accelerated uncertainty quantificat
Mode-based model-reduction is used to reduce the degrees of freedom of high dimensional systems, often by describing the system state by a linear combination of spatial modes. Transport dominated phenomena, ubiquitous in technical and scientific appl