Reconstructed Discontinuous Galerkin Methods for Hyperbolic Diffusion Equations on Unstructured Grids (Communications in Computational Physics, 2019)
Reconstructed Discontinuous Galerkin (rDG) methods are presented for solving diffusion equations based on a first-order hyperbolic system (FOHS) formulation.The idea is to combine the advantages of the FOHS formulation and the rDG methodsin an effort to develop a more reliable, accurate, efficient, and robust method for solving the diffusion equations. The developed hyperbolic rDG methods can be made tohave higher-order accuracy than conventional DG methods with fewer degrees of freedom. A number of test cases for different diffusion equations are presented to assessaccuracy and performance of the newly developed hyperbolic rDG methods in comparison with the standard BR2 DG method. Numerical experiments demonstrate thatthe hyperbolic rDG methods are able to achieve the designed optimal order of accuracy for both solutions and their derivatives on regular, irregular, and heterogeneousgirds, and outperform the BR2 method in terms of the magnitude of the error, the orderof accuracy, the size of time steps, and the CPU times required to achieve steady statesolutions, indicating that the developed hyperbolic rDG methods provide an attractiveand probably an even superior alternative for solving the diffusion equations.
Keywords: Discontinuous Galerkin methods; first-order hyperbolic system; unstructured grids.