Total-variation-diminishing time discretizations
SIAM Journal on Scientific and Statistical Computing
Summation by parts for finite difference approximations for d/dx
Journal of Computational Physics
Weighted essentially non-oscillatory schemes
Journal of Computational Physics
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
Discrete Shocks for Finite Difference Approximations to Scalar Conservation Laws
SIAM Journal on Numerical Analysis
A stable and conservative interface treatment of arbitrary spatial accuracy
Journal of Computational Physics
Low-storage, explicit Runge-Kutta schemes for the compressible Navier-Stokes equations
Applied Numerical Mathematics
Optimized weighted essentially nonoscillatory schemes for linear waves with discontinuity: 381
Journal of Computational Physics
SIAM Journal on Numerical Analysis
Mapped weighted essentially non-oscillatory schemes: Achieving optimal order near critical points
Journal of Computational Physics
Journal of Computational Physics
An improved weighted essentially non-oscillatory scheme for hyperbolic conservation laws
Journal of Computational Physics
Convergence of Godunov-Type Schemes for Scalar Conservation Laws under Large Time Steps
SIAM Journal on Numerical Analysis
Third-order Energy Stable WENO scheme
Journal of Computational Physics
Journal of Computational Physics
An adaptive central-upwind weighted essentially non-oscillatory scheme
Journal of Computational Physics
Journal of Computational Physics
Analysis of WENO Schemes for Full and Global Accuracy
SIAM Journal on Numerical Analysis
Journal of Computational Physics
High-order entropy stable finite difference schemes for nonlinear conservation laws: Finite domains
Journal of Computational Physics
Journal of Scientific Computing
A generalized framework for nodal first derivative summation-by-parts operators
Journal of Computational Physics
Hi-index | 31.48 |
A third-order Energy Stable Weighted Essentially Non-Oscillatory (ESWENO) finite difference scheme developed by the authors of this paper [N.K. Yamaleev, M.H. Carpenter, Third-order energy stable WENO scheme, J. Comput. Phys. 228 (2009) 3025-3047] was proven to be stable in the energy norm for both continuous and discontinuous solutions of systems of linear hyperbolic equations. Herein, a systematic approach is presented that enables ''energy stable'' modifications for existing WENO schemes of any order. The technique is demonstrated by developing a one-parameter family of fifth-order upwind-biased ESWENO schemes including one sixth-order central scheme; ESWENO schemes up to eighth order are presented in the Appendix. We also develop new weight functions and derive constraints on their parameters, which provide consistency, much faster convergence of the high-order ESWENO schemes to their underlying linear schemes for smooth solutions with arbitrary number of vanishing derivatives, and better resolution near strong discontinuities than the conventional counterparts.