A hybrid ENO reconstruction with limiters for systems of hyperbolic conservation laws

Abstract

We consider a new class of essentially non-oscillatory (ENO) piecewise polynomial reconstructions together with interpolants based on Monotone Upwind Schemes for Conservation Laws. We improve the second-order ENO polynomial reconstruction by choosing an additional point inside the stencil in order to obtain the highest accuracy when combined with various non-linear limiters. The resulting algorithms are based on only one stencil selection, and we show that they can be efficiently implemented with largest allowable CFL numbers using optimal strong stability-preserving Runge-Kutta time evolution methods. The numerical results indicate that in some cases the schemes yield errors smaller in magnitude as compared to the fourth-order ENO scheme.