Efficient implementation of essentially non-oscillatory shock-capturing schemes
Journal of Computational Physics
Efficient implementation of essentially non-oscillatory shock-capturing schemes,II
Journal of Computational Physics
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
Approximate Riemann solvers, parameter vectors, and difference schemes
Journal of Computational Physics - Special issue: commenoration of the 30th anniversary
Journal of Computational Physics
Mapped weighted essentially non-oscillatory schemes: Achieving optimal order near critical points
Journal of Computational Physics
Journal of Computational Physics
Third-order Energy Stable WENO scheme
Journal of Computational Physics
Applied Numerical Mathematics
A systematic methodology for constructing high-order energy stable WENO schemes
Journal of Computational Physics
On the HLLC Riemann solver for interface interaction in compressible multi-fluid flow
Journal of Computational Physics
Journal of Computational Physics
High-order conservative finite difference GLM-MHD schemes for cell-centered MHD
Journal of Computational Physics
An adaptive central-upwind weighted essentially non-oscillatory scheme
Journal of Computational Physics
Approximation error of the Lagrange reconstructing polynomial
Journal of Approximation Theory
High order weighted essentially non-oscillatory WENO-Z schemes for hyperbolic conservation laws
Journal of Computational Physics
A Speed-Up Strategy for Finite Volume WENO Schemes for Hyperbolic Conservation Laws
Journal of Scientific Computing
Improvement of Convergence to Steady State Solutions of Euler Equations with the WENO Schemes
Journal of Scientific Computing
Multi-domain Fourier-continuation/WENO hybrid solver for conservation laws
Journal of Computational Physics
Analysis of WENO Schemes for Full and Global Accuracy
SIAM Journal on Numerical Analysis
Binary weighted essentially non-oscillatory (BWENO) approximation
Journal of Computational and Applied Mathematics
A New Mapped Weighted Essentially Non-oscillatory Scheme
Journal of Scientific Computing
Journal of Scientific Computing
An improved weighted essentially non-oscillatory scheme with a new smoothness indicator
Journal of Computational Physics
Accuracy of the weighted essentially non-oscillatory conservative finite difference schemes
Journal of Computational Physics
Journal of Scientific Computing
A third-order accurate direct Eulerian GRP scheme for the Euler equations in gas dynamics
Journal of Computational Physics
Hi-index | 31.51 |
In this article we develop an improved version of the classical fifth-order weighted essentially non-oscillatory finite difference scheme of [G.S. Jiang, C.W. Shu, Efficient implementation of weighted ENO schemes, J. Comput. Phys. 126 (1996) 202-228] (WENO-JS) for hyperbolic conservation laws. Through the novel use of a linear combination of the low order smoothness indicators already present in the framework of WENO-JS, a new smoothness indicator of higher order is devised and new non-oscillatory weights are built, providing a new WENO scheme (WENO-Z) with less dissipation and higher resolution than the classical WENO. This new scheme generates solutions that are sharp as the ones of the mapped WENO scheme (WENO-M) of Henrick et al. [A.K. Henrick, T.D. Aslam, J.M. Powers, Mapped weighted essentially non-oscillatory schemes: achieving optimal order near critical points, J. Comput. Phys. 207 (2005) 542-567], however with a 25% reduction in CPU costs, since no mapping is necessary. We also provide a detailed analysis of the convergence of the WENO-Z scheme at critical points of smooth solutions and show that the solution enhancements of WENO-Z and WENO-M at problems with shocks comes from their ability to assign substantially larger weights to discontinuous stencils than the WENO-JS scheme, not from their superior order of convergence at critical points. Numerical solutions of the linear advection of discontinuous functions and nonlinear hyperbolic conservation laws as the one dimensional Euler equations with Riemann initial value problems, the Mach 3 shock-density wave interaction and the blastwave problems are compared with the ones generated by the WENO-JS and WENO-M schemes. The good performance of the WENO-Z scheme is also demonstrated in the simulation of two dimensional problems as the shock-vortex interaction and a Mach 4.46 Richtmyer-Meshkov Instability (RMI) modeled via the two dimensional Euler equations.