Previous theoretical (McCartin 1989a) and computational (McCartin 1989b) results on exponential splines are herein applied to provide approximate solutions of high order accuracy to nonlinear hyperbolic conservation laws. The automatic selection of certain "tension" parameters associated with the exponential spline allows the sharp resolution of shocks and the suppression of any attendant oscil...

An Entropy-based nonlinear viscosity for approximating conservation laws using Fourier expansions is proposed. The viscosity is proportional to the entropy residual of the equation (or system) and thus preserves the spectral accuracy of the method. To cite this article: J.-L. Guermond, R. Pasquetti, C. R. Acad. Sci. Paris, Ser. I 346 (2008). © 2008 Académie des sciences. Published by Elsevier M...

We study the limiting behavior of the solutions to a class of conservation laws with vanishing nonlinear diffusion and dispersion terms. We prove the convergence to the entropy solution of the first order problem under a condition on the relative size of the diffusion and the dispersion terms. This work is motivated by the pseudo-viscosity approximation introduced by Von Neumann in the 50’s.

We consider multidimensional hyperbolic systems of conservation laws with relaxation, together with their associated limit systems. A strong stability condition for such asymptotics has been introduced by Chen, Levermore, Liu in Comm. Pure Appl. Math. 47, 787-830, namely the existence of an entropy extension. We propose here a new stability condition, the reduced stability condition, which is w...

We present a new, formally third order, implicit Weighted Essentially NonOscillatory (iWENO3) finite volume scheme for solving systems of nonlinear conservation laws. We then generalize it to define an implicit Eulerian-Lagrangian WENO (iEL-WENO) scheme. Implicitness comes from the use of an implicit Runge-Kutta (RK) time integrator. A specially chosen two-stage RK method allows us to drastical...