Journal of Computational Physics
Dispersion-relation-preserving finite difference schemes for computational acoustics
Journal of Computational Physics
The stability of numerical boundary treatments for compact high-order finite-difference schemes
Journal of Computational Physics
Parallel, adaptive finite element methods for conservation laws
Proceedings of the third ARO workshop on Adaptive methods for partial differential equations
High-order finite element methods for singularly perturbed elliptic and parabolic problems
SIAM Journal on Applied Mathematics
Low-dissipation and low-dispersion Runge-Kutta schemes for computational acoustics
Journal of Computational Physics
Journal of Computational Physics
Prefactored small-stencil compact schemes
Journal of Computational Physics
Devising discontinuous Galerkin methods for non-linear hyperbolic conversation laws
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. VII: partial differential equations
A Stable, perfectly matched layer for linearized Euler equations in unslit physical variables
Journal of Computational Physics
Spectral (finite) volume method for conservation laws on unstructured grids: basic formulation
Journal of Computational Physics
Aspects of discontinuous Galerkin methods for hyperbolic conservation laws
Finite Elements in Analysis and Design - Robert J. Melosh medal competition
Journal of Computational Physics
Journal of Computational Physics
Spectral difference method for unstructured grids I: basic formulation
Journal of Computational Physics
Short Note: On the connection between the spectral volume and the spectral difference method
Journal of Computational Physics
Journal of Computational Physics
Spatial and spectral superconvergence of discontinuous Galerkin method for hyperbolic problems
Journal of Computational and Applied Mathematics
A sparse and high-order accurate line-based discontinuous Galerkin method for unstructured meshes
Journal of Computational Physics
Hi-index | 31.47 |
In this paper we formulate a numerical method that is high order with strong accuracy for numerical wave numbers, and is adaptive to non-uniform grids. Such a method is developed based on the discontinuous Galerkin method (DGM) applied to the hyperbolic equation, resulting in finite difference type schemes applicable to non-uniform grids. The schemes will be referred to as DGM-FD schemes. These schemes inherit naturally some features of the DGM, such as high-order approximations, applicability to non-uniform grids and super-accuracy for wave propagations. Stability of the schemes with boundary closures is investigated and validated. Proposed scheme is demonstrated by numerical examples including the linearized acoustic waves and solutions of non-linear Burger's equation and the flat-plate boundary layer problem. For non-linear equations, proposed flux finite difference formula requires no explicit upwind and downwind split of the flux. This is in contrast to existing upwind finite difference schemes in the literature.