Hong Luo

TL;DR: The numerical results obtained indicate that the use of the GMRES+LU-SGS method leads to a significant increase in performance over the best current implicit methods, GM RES+ILU and LU-S GS, while maintaining memory requirements similar to its explicit counterpart.

TL;DR: A weighted essentially non-oscillatory reconstruction scheme based on Hermite polynomials is developed and applied as a limiter for the discontinuous Galerkin finite element method on unstructured grids to demonstrate the accuracy, effectiveness, and robustness of the designed HWENO limiter.

TL;DR: The numerical results demonstrated the superior accuracy of this discontinuous Galerkin method in comparison with a second order finite volume method and a third-order WENO method, indicating its promise and potential to become not just a competitive but simply a superior approach than its finite volume and ENO/WENO counterparts for solving flow problems of scientific and industrial interest.

TL;DR: The numerical results indicate that this reconstruction-based discontinuous Galerkin (RDG) method is able to deliver the same accuracy as the well-known Bassi-Rebay II scheme, at a half of its computing costs for the discretization of the viscous fluxes in the Navier-Stokes equations, clearly demonstrating its superior performance over the existing DG methods.

TL;DR: A p-multigrid (p = polynomial degree) discontinuous Galerkin method is presented for the solution of the compressible Euler equations on unstructured grids, resulting in an accurate, fast, and low memory method that can be used to accelerate the convergence of the Euler equation to a steady state for discontinuousGalerkin methods.