Uniformly high order accurate essentially non-oscillatory schemes, 111
Journal of Computational Physics
Total-variation-diminishing time discretizations
SIAM Journal on Scientific and Statistical Computing
A finite-volume high-order ENO scheme for two-dimensional hyperbolic systems
Journal of Computational Physics
On a cell entropy inequality for discontinuous Galerkin methods
Mathematics of Computation
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
A Stable Penalty Method for the Compressible Navier--Stokes Equations: I. Open Boundary Conditions
SIAM Journal on Scientific Computing
Spectral methods on arbitrary grids
Journal of Computational Physics
Discrete Shocks for Finite Difference Approximations to Scalar Conservation Laws
SIAM Journal on Numerical Analysis
Journal of Computational Physics
SIAM Journal on Numerical Analysis
A stable and conservative interface treatment of arbitrary spatial accuracy
Journal of Computational Physics
Weighted essentially non-oscillatory schemes on triangular meshes
Journal of Computational Physics
Journal of Computational Physics
Optimized weighted essentially nonoscillatory schemes for linear waves with discontinuity: 381
Journal of Computational Physics
Compact Central WENO Schemes for Multidimensional Conservation Laws
SIAM Journal on Scientific Computing
SIAM Journal on Numerical Analysis
Journal of Computational Physics
Stable and Accurate Artificial Dissipation
Journal of Scientific Computing
Runge--Kutta Discontinuous Galerkin Method Using WENO Limiters
SIAM Journal on Scientific Computing
Mapped weighted essentially non-oscillatory schemes: Achieving optimal order near critical points
Journal of Computational Physics
Journal of Computational Physics
A Hermite WENO-based limiter for discontinuous Galerkin method on unstructured grids
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
A systematic methodology for constructing high-order energy stable WENO schemes
Journal of Computational Physics
High-order conservative finite difference GLM-MHD schemes for cell-centered MHD
Journal of Computational Physics
Revisiting and Extending Interface Penalties for Multi-domain Summation-by-Parts Operators
Journal of Scientific Computing
High order weighted essentially non-oscillatory WENO-Z schemes for hyperbolic conservation laws
Journal of Computational Physics
Journal of Computational Physics
Lax-Friedrichs fast sweeping methods for steady state problems for hyperbolic conservation laws
Journal of Computational Physics
A new gas-kinetic scheme based on analytical solutions of the BGK equation
Journal of Computational Physics
Accuracy of the weighted essentially non-oscillatory conservative finite difference schemes
Journal of Computational Physics
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 | 31.49 |
A new third-order Energy Stable Weighted Essentially Non-Oscillatory (ESWENO) finite difference scheme for scalar and vector hyperbolic equations with piecewise continuous initial conditions is developed. The new scheme is proven to be linearly stable in the energy norm for both continuous and discontinuous solutions. In contrast to the existing high-resolution shock-capturing schemes, no assumption that the reconstruction should be total variation bounded (TVB) is explicitly required to prove stability of the new scheme. We also present new weight functions which drastically improve the accuracy of the third-order ESWENO scheme. Based on a truncation error analysis, we show that the ESWENO scheme is design-order accurate for smooth solutions with any number of vanishing derivatives, if its tuning parameters satisfy certain constraints. Numerical results show that the new ESWENO scheme is stable and significantly outperforms the conventional third-order WENO scheme of Jiang and Shu in terms of accuracy, while providing essentially non-oscillatory solutions near strong discontinuities.