Adaptive Radiation Transport
Radiative transfer is cpu-intensive, especially in realistic geometries. A method to reduce computational cost is to refine the spatial mesh in those regions where the solution contains more detail. We have studied both regular and goal-oriented (adjoint) spatially adaptive procedures. Mesh refinement (and coarsening) is based on hierarchical meshes of various element types (triangles, quadrilateral, tetrahedral, hexahedra).
Adaptive resolution of radiation transport in space is relatively straightforward to achieve. Angular refinement is still an active area of research. Traditional discrete ordinates methods do not allow for local angular refinement by nature of their construction. The same is true for the spherical harmonics approach. Discrete ordinates based on product quadrature allow for a locally dense distribution of directions, but only centered on a particular direction. We study angular refinement based on tessellations of the directional sphere combined with a discontinuous finite element space. This has the advantage of offering arbitrary hierarchic refinement. These methods are pursued for neutral particle transport as well as for protons where a Fokker-Planck scatter model is used on locally refined angular meshes.
D. Lathouwers, Goal-oriented spatial adaptivity for the SN equations on unstructured triangular meshes, Annals of Nuclear Energy 38(6), pp. 1373-1381, 2011.
D. Lathouwers, Spatially adaptive eigenvalue estimation for the SN equations on unstructured triangular meshes, Annals of Nuclear Energy 38(9), pp. 1867-1876, 2011.
J. Kophazi and D. Lathouwers, A space-angle DGFEM approach for the Boltzmann radiation transport equation with local angular refinement, Journal of Computational Physics 297, pp. 637-668, 2015.