Efficient implementation of essentially non-oscillatory shock-capturing schemes,II
Journal of Computational Physics
ENO schemes with subcell resolution
Journal of Computational Physics
An artificial compression method for ENO schemes: the slope modification method
Journal of Computational Physics
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
A MUSCL method satisfying all the numerical entropy inequalities
Mathematics of Computation
Contact Discontinuity Capturing Schemes for Linear Advection and Compressible Gas Dynamics
Journal of Scientific Computing
Runge–Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems
Journal of Scientific Computing
Entropy Satisfaction of a Conservative Shock-Tracking Method
SIAM Journal on Numerical Analysis
Anti-diffusive flux corrections for high order finite difference WENO schemes
Journal of Computational Physics
Two-Dimensional Extension of the Reservoir Technique for Some Linear Advection Systems
Journal of Scientific Computing
Entropy-TVD Scheme for Nonlinear Scalar Conservation Laws
Journal of Scientific Computing
Hi-index | 0.01 |
In a recent work J. Sci. Comput. 16, 479–524 (2001), B. Després and F. Lagoutière introduced a new approach to derive numerical schemes for hyperbolic conservation laws. Its most important feature is the ability to perform an exact resolution for a single traveling discontinuity. However their scheme is not entropy satisfying and can keep nonentropic discontinuities. The purpose of our work is, starting from the previous one, to introduce a new class of schemes for monotone scalar conservation laws, that satisfy an entropy inequality, while still resolving exactly the single traveling shocks or contact discontinuities. We show that it is then possible to have an excellent resolution of rarefaction waves, and also to avoid the undesirable staircase effect. In practice, our numerical experiments show second-order accuracy.