Uniformly high order accurate essentially non-oscillatory schemes, 111
Journal of Computational Physics
On essentially non-oscillatory schemes on unstructured meshes: analysis and implementation
Journal of Computational Physics
Weighted essentially non-oscillatory schemes
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Average-state Jacobians and implicit methods for compressible viscous and turbulent flows
Journal of Computational Physics
High-order accurate discontinuous finite element solution of the 2D Euler equations
Journal of Computational Physics
The Runge-Kutta discontinuous Galerkin method for conservation laws V multidimensional systems
Journal of Computational Physics
Journal of Computational Physics
A fast, matrix-free implicity method for compressible flows on unstructured grids
Journal of Computational Physics
Weighted essentially non-oscillatory schemes on triangular meshes
Journal of Computational Physics
On the use of higher-order finite-difference schemes on curvilinear and deforming meshes
Journal of Computational Physics
Journal of Computational Physics
Runge--Kutta Discontinuous Galerkin Method Using WENO Limiters
SIAM Journal on Scientific Computing
ADER schemes for three-dimensional non-linear hyperbolic systems
Journal of Computational Physics
A p-multigrid discontinuous Galerkin method for the Euler equations on unstructured grids
Journal of Computational Physics
A Hermite WENO-based limiter for discontinuous Galerkin method on unstructured grids
Journal of Computational Physics
Journal of Computational Physics
A vertex-based hierarchical slope limiter for p-adaptive discontinuous Galerkin methods
Journal of Computational and Applied Mathematics
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
Hierarchical slope limiting in explicit and implicit discontinuous Galerkin methods
Journal of Computational Physics
Hi-index | 31.49 |
A discontinuous Galerkin method based on a Taylor basis is presented for the solution of the compressible Euler equations on arbitrary grids. Unlike the traditional discontinuous Galerkin methods, where either standard Lagrange finite element or hierarchical node-based basis functions are used to represent numerical polynomial solutions in each element, this DG method represents the numerical polynomial solutions using a Taylor series expansion at the centroid of the cell. Consequently, this formulation is able to provide a unified framework, where both cell-centered and vertex-centered finite volume schemes can be viewed as special cases of this discontinuous Galerkin method by choosing reconstruction schemes to compute the derivatives, offer the insight why the DG methods are a better approach than the finite volume methods based on either TVD/MUSCL reconstruction or essentially non-oscillatory (ENO)/weighted essentially non-oscillatory (WENO) reconstruction, and has a number of distinct, desirable, and attractive features, which can be effectively used to address some of shortcomings of the DG methods. The developed method is used to compute a variety of both steady-state and time-accurate flow problems on arbitrary grids. 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.