Oliver Sutton: Thursday 3 June at 11:00 am
ABSTRACT:
The linear Boltzmann problem is a widely used model for the transport of particles through a scattering medium, such as neutrons in a nuclear reactor, or photons during radiotherapy or in the atmosphere of a star. The key challenge in simulating such phenomena using this model lies in the fact that the problem is an integro-partial-differential equation in 6 independent variables: three position variables and three momentum variables (7 if time is also included). Despite this, there is a long history of this model being successfully applied in practice. A well-studied class of numerical schemes for simulating phenomena governed by this model couples a discontinuous Galerkin spatial discretisation with a multigroup discrete-ordinates discretisation in the momentum variables. Standard multigroup discrete ordinates discretisations may be viewed as employing a piecewise constant approximation space, and possess the particularly attractive characteristic of decoupling the fully-coupled problem into a sequence of three-dimensional linear transport problems which may be solved independently and in parallel.
In this talk, we will discuss a new generalisation of these multigroup discrete ordinates schemes. These new schemes employ arbitrarily high order polynomials in the discretisation of the momentum variables, providing high order convergence properties, and offer a familiar Galerkin framework for their analysis. Crucially, moreover, they retain the simple algorithmic structure of their classical counterparts.
