COMPARING THE DISCONTINUOUS GALERKIN AND HIGH-ORDER DIAMOND DIFFERENCING METHODS FOR THE TRANSPORT EQUATION ON A LOZENGE-BASED HEXAGONAL GEOMETRY

This paper presents an implementation and a comparison of two spatial discretisation schemes over hexagonal geometry for the two-dimensional discrete ordinates transport equation. The methods are high-order Discontinuous Galerkin (DG) finite element scheme Diamond Differencing (DD) scheme. DG method has been, is being, studied on geometry, also called honeycomb mesh – but not DD method. In this research effort, it was chosen to divide hexagons into (at least) three lozenges. An affine transformation then applied onto said lozenges cast them reference quadrilaterals usually in elements. practice, effectively means that equations used Cartesian have their terms operators altered using Jacobian matrix transformation. implemented solver code DRAGON5. Two 2D benchmark problems were verification validation, including one based Monju 3D reactor benchmark. It found diamond-differencing seemed better. converged much faster towards solution at comparable refinements first-order expansion flux. Even if difference present second-order, slower, about four times slower.