Journal of Computational Physics
High-order accurate discontinuous finite element solution of the 2D Euler equations
Journal of Computational Physics
The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
SIAM Journal on Numerical Analysis
A discontinuous Galerkin method for the viscous MHD equations
Journal of Computational Physics
An efficient implicit discontinuous spectral Galerkin method
Journal of Computational Physics
A p-multigrid discontinuous Galerkin method for the Euler equations on unstructured grids
Journal of Computational Physics
Journal of Computational Physics
A Hermite WENO-based limiter for discontinuous Galerkin method on unstructured grids
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Very high order PNPM schemes on unstructured meshes for the resistive relativistic MHD equations
Journal of Computational Physics
Stability analysis of the cell centered finite-volume Muscl method on unstructured grids
Numerische Mathematik
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
A class of hybrid DG/FV methods for conservation laws II: Two-dimensional cases
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.45 |
A reconstructed discontinuous Galerkin (RDG) method based on a hierarchical WENO reconstruction, termed HWENO (P"1P"2) in this paper, designed not only to enhance the accuracy of discontinuous Galerkin methods but also to ensure the nonlinear stability of the RDG method, is presented for solving the compressible Euler equations on tetrahedral grids. In this HWENO (P"1P"2) method, a quadratic polynomial solution (P"2) is first reconstructed using a Hermite WENO reconstruction from the underlying linear polynomial (P"1) discontinuous Galerkin solution to ensure the linear stability of the RDG method and to improve the efficiency of the underlying DG method. By taking advantage of handily available and yet invaluable information, namely the derivatives in the DG formulation, the stencils used in the reconstruction involve only von Neumann neighborhood (adjacent face-neighboring cells) and thus are compact. The first derivatives of the quadratic polynomial solution are then reconstructed using a WENO reconstruction in order to eliminate spurious oscillations in the vicinity of strong discontinuities, thus ensuring the nonlinear stability of the RDG method. The developed HWENO (P"1P"2) method is used to compute a variety of flow problems on tetrahedral meshes to demonstrate its accuracy, robustness, and non-oscillatory property. The numerical experiments indicate that the HWENO (P"1P"2) method is able to capture shock waves within one cell without any spurious oscillations, and achieve the designed third-order of accuracy: one order accuracy higher than the underlying DG method.