An Adaptive Moving Mesh Discontinuous Galerkin Method for the Radiative Transfer Equation (Communications in Computational Physics, 2020)
The radiative transfer equation models the interaction of radiation with scattering and absorbing media and has important applications in various fields in scienceand engineering. It is an integro-differential equation involving time, frequency, spaceand angular variables and contains an integral term in angular directions while being hyperbolic in space. The challenges for its numerical solution include the needsto handle with its high dimensionality, the presence of the integral term, and the development of discontinuities and sharp layers in its solution along spatial directions.Its numerical solution is studied in this paper using an adaptive moving mesh discontinuous Galerkin method for spatial discretization together with the discrete ordinatemethod for angular discretization. The former employs a dynamic mesh adaptationstrategy based on moving mesh partial differential equations to improve computational accuracy and efficiency. Its mesh adaptation ability, accuracy, and efficiency aredemonstrated in a selection of one- and two-dimensional numerical examples.
Keywords: Adaptive moving mesh; discontinuous Galerkin method; radiative transfer equation; high order accuracy; high resolution.