Low-Memory, Discrete Ordinates, Discontinuous Galerkin Methods for Radiative Transport

Discontinuous Galerkin Methods for the Radiative Transport Equation

This notes presents some recent results regarding the approximation of the linear radiative transfer equation using discontinuous Galerkin methods. The locking effect occurring in the diffusion limit with the upwind numerical flux is investigated and a correction technique is proposed.

On discontinuous Galerkin and discrete ordinates approximations for neutron transport equation and the critical eigenvalue

Discrete-Ordinate Discontinuous Galerkin Methods for Solving the Radiative Transfer Equation

Abstract. The radiative transfer equation (RTE) occurs in a wide variety of applications. In this paper, we study discrete-ordinate discontinuous Galerkin methods for solving the RTE. The numerical methods are formed in two steps. In the first step, the discrete ordinate technique is applied to discretize the integral operator for the angular variable, resulting in a semi-discrete hyperbolic sy...

Sparse Discrete Ordinates Method in Radiative Transfer

The stationary monochromatic radiative transfer equation (RTE) is a partial differential transport equation stated on a five-dimensional phase space, the Cartesian product of physical and angular domain. We solve the RTE with a Galerkin FEM in physical space and collocation in angle, corresponding to a discrete ordinates method (DOM). To reduce the complexity of the problem and to avoid the “cu...

Discontinuous Galerkin methods for coupled flow and reactive transport problems

Primal discontinuous Galerkin methods with interior penalty are proposed to solve the coupled system of flow and reactive transport in porous media, which arises from many applications including miscible displacement and acid-stimulated flow. A cut-off operator is introduced in the discontinuous Galerkin schemes to treat the coupling of flow and transport and the coupling of transport and react...