R-Z Geometry Discrete Ordinates Radiation Transport Using Higher-Order Finite Element Spatial Discretizations on Meshes with Curved Surfaces

Abstract

We spatially discretize the discrete ordinates radiation transport equation using high-order discontinuous Galerkin finite elements in R-Z geometry. Previous research has demonstrated first-order methods have 2nd-order spatial convergence rates in R-Z geometry. Presently, we demonstrate that higher-order (HO) methods preserve the p + 1 convergence rates on smooth solutions, where p is the finite element order. Further, we extend the use of HO finite element methods to utilize meshes with curved surfaces. We also demonstrate that meshes with curved surfaces do not degrade the observed spatial convergence rates. Finally, we exercise the methodology on a highly diffusive and scattering problem with alternating incident boundaries to show that both HO methods and mesh refinement reduce the negative scalar fluxes that result from oscillations.

Keywords:

• Radiation transport
• high-order finite elements
• meshes with curved surfaces

Acknowledgments

The authors wish to thank Tom Brunner for his significant contributions to our transport code. This work performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344. Document number LA-UR-19-21726.