Uniformly high order accurate essentially non-oscillatory schemes, 111
Journal of Computational Physics
Journal of Computational Physics
On essentially non-oscillatory schemes on unstructured meshes: analysis and implementation
Journal of Computational Physics
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
Journal of Computational Physics
Weighted essentially non-oscillatory schemes on triangular meshes
Journal of Computational Physics
Runge–Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems
Journal of Scientific Computing
Spectral (finite) volume method for conservation laws on unstructured grids: basic formulation
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
A p-multigrid discontinuous Galerkin method for the Euler equations on unstructured grids
Journal of Computational Physics
Spectral difference method for unstructured grids I: basic formulation
Journal of Computational Physics
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
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.46 |
By comparing the discontinuous Galerkin (DG) methods, the k-exact finite volume (FV) methods and the lift collocation penalty (LCP) methods, a concept of 'static reconstruction' and 'dynamic reconstruction' was introduced for higher-order numerical methods in our previous work. Based on this concept, a class of hybrid DG/FV methods was presented for one-dimensional conservation law using a 'hybrid reconstruction' approach. In the hybrid DG/FV schemes, the lower-order derivatives of the piecewise polynomial are computed locally in a cell by the traditional DG method (called as 'dynamic reconstruction'), while the higher-order derivatives are re-constructed by the 'static reconstruction' of the FV method, using the known lower-order derivatives in the cell itself and in its adjacent face neighboring cells. In this follow-up paper, the hybrid DG/FV schemes are extended onto two-dimensional unstructured and hybrid grids. The two-dimensional linear and non-linear scalar conservation law and Euler equations are considered. Some typical cases are tested to demonstrate the performance of the hybrid DG/FV method, and the numerical results show that they can reduce the CPU time and memory requirement greatly than the traditional DG method with the same order of accuracy in the same mesh.