Summation by parts for finite difference approximations for d/dx
Journal of Computational Physics
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
A stable and conservative interface treatment of arbitrary spatial accuracy
Journal of Computational Physics
Journal of Scientific Computing
On the order of accuracy for difference approximations of initial-boundary value problems
Journal of Computational Physics
Optimised boundary compact finite difference schemes for computational aeroacoustics
Journal of Computational Physics
Journal of Computational Physics
Third-order Energy Stable WENO scheme
Journal of Computational Physics
A systematic methodology for constructing high-order energy stable WENO schemes
Journal of Computational Physics
Revisiting and Extending Interface Penalties for Multi-domain Summation-by-Parts Operators
Journal of Scientific Computing
Journal of Computational Physics
A Robust Reconstruction for Unstructured WENO Schemes
Journal of Scientific Computing
High-order entropy stable finite difference schemes for nonlinear conservation laws: Finite domains
Journal of Computational Physics
A generalized framework for nodal first derivative summation-by-parts operators
Journal of Computational Physics
Hi-index | 31.46 |
A general strategy was presented in 2009 by Yamaleev and Carpenter for constructing energy stable weighted essentially non-oscillatory (ESWENO) finite-difference schemes on periodic domains. ESWENO schemes up to eighth order were developed that are stable in the energy norm for systems of linear hyperbolic equations. Herein, boundary closures are developed for the fourth-order ESWENO scheme that maintain, wherever possible, the WENO stencil biasing properties and satisfy the summation-by-parts (SBP) operator convention, thereby ensuring stability in an L"2 norm. Second-order and third-order boundary closures are developed that are stable in diagonal and block norms, respectively, and achieve third- and fourth-order global accuracy for hyperbolic systems. A novel set of nonuniform flux interpolation points is necessary near the boundaries to simultaneously achieve (1) accuracy, (2) the SBP convention, and (3) WENO stencil biasing mechanics.