An efficient reconstruction algorithm for diffusion on triangular grids using the nodal discontinuous Galerkin method

High-energy-density (HED) hydrodynamics studies such as those relevant to inertial confinement fusion and astrophysics require highly disparate densities, temperatures, viscosities, other diffusion parameters over relatively short spatial scales. This presents a challenge for high-order accurate methods effectively resolve the at these scales, particularly in presence of diffusion. A significant volume engineering physics applications use an unstructured discontinuous Galerkin (DG) method developed based on finite element mesh generation algorithmic framework. work discusses application affine reconstructed nodal DG grids triangles. Solving terms is non-trivial due solution representations being piecewise continuous. Hence, diffusive flux not defined interface elements. The proposed numerical approach reconstructs smooth parallelogram that enclosed by quadrilateral formed two adjacent triangle between triangles diagonal parallelogram. Similar triangles, mapping parallelograms from physical domain reference mapping, which necessary efficient implementation algorithm. Thus, all computations can still be performed domain, promotes efficiency computation storage. reconstruction does make assumptions choice polynomial basis. Reconstructed algorithms have previously been modal implementations convection–diffusion equations. However, best authors’ knowledge, this first practical guideline has applying algorithm with focus accuracy efficiency. demonstrated number benchmark cases well challenging substantive problem HED parameters.