A Discrete Ordinates Algorithm for Domains with Embedded Boundaries

Louis H. Howell

Vincent E. Beckner


Embedded boundary methods model fluid flows in complex geometries by treating boundaries as tracked interfaces in a regular mesh. Though often referred to as ``Cartesian grid'' methods, they are equally well-suited to axisymmetric problems. This paper describes a formulation of the discrete ordinates method for radiative transfer calculations with embedded boundaries. The method uses diamond-difference stencils in the interior with a conservative extension to boundary cells based on a volume-of-fluid approach. Numerical examples are presented in both 2D Cartesian and axisymmetric geometries, including a model of the BERL 300kW natural gas burner.