A technique of treating negative weights in WENO schemes
Journal of Computational Physics
Numerical Entropy Production on Shocks and Smooth Transitions
Journal of Scientific Computing
Journal of Computational Physics
High-order semi-discrete central-upwind schemes for multi-dimensional Hamilton--Jacobi equations
Journal of Computational Physics
A central-constrained transport scheme for ideal magnetohydrodynamics
Journal of Computational Physics
Central schemes on overlapping cells
Journal of Computational Physics
On the Total Variation of High-Order Semi-Discrete Central Schemes for Conservation Laws
Journal of Scientific Computing
A Hermite upwind WENO scheme for solving hyperbolic conservation laws
Journal of Computational Physics
A central WENO scheme for solving hyperbolic conservation laws on non-uniform meshes
Journal of Computational Physics
A new fourth-order non-oscillatory central scheme for hyperbolic conservation laws
Applied Numerical Mathematics
A central conservative scheme for general rectangular grids
Journal of Computational Physics
Third-order Energy Stable WENO scheme
Journal of Computational Physics
A high-order multi-dimensional HLL-Riemann solver for non-linear Euler equations
Journal of Computational Physics
Solving the euler equations on graphics processing units
ICCS'06 Proceedings of the 6th international conference on Computational Science - Volume Part IV
New adaptive artificial viscosity method for hyperbolic systems of conservation laws
Journal of Computational Physics
A HLL-Rankine-Hugoniot Riemann solver for complex non-linear hyperbolic problems
Journal of Computational Physics
A re-averaged WENO reconstruction and a third order CWENO scheme for hyperbolic conservation laws
Journal of Computational Physics
Hi-index | 0.07 |
We present a new third-order central scheme for approximating solutions of systems of conservation laws in one and two space dimensions. In the spirit of Godunov-type schemes, our method is based on reconstructing a piecewise-polynomial interpolant from cell-averages which is then advanced exactly in time.In the reconstruction step, we introduce a new third-order, compact, central weighted essentially nonoscillatory (CWENO) reconstruction, which is written as a convex combination of interpolants based on different stencils. The heart of the matter is that one of these interpolants is taken as a suitable quadratic polynomial, and the weights of the convex combination are set as to obtain third-order accuracy in smooth regions. The embedded mechanism in the WENO-like schemes guarantees that in regions with discontinuities or large gradients, there is an automatic switch to a one-sided second-order reconstruction, which prevents the creation of spurious oscillations.In the one-dimensional case, our new third-order reconstruction is based on an extremely compact three-point stencil. Analogous compactness is retained in more space dimensions. The accuracy, robustness, and high-resolution properties of our scheme are demonstrated in a variety of one- and two-dimensional problems.