A novel second order accurate hybrid numerical approach for conservation laws

In this paper, we present a novel one-parameter hybrid scheme for hyperbolic systems of conservation laws. The parameter value can be adapted in each numerical cell in order to obtain the advantages of Lax-Wendroff flux (second order scheme) where the solution is locally smooth. On the other hand, the scheme can switch to the Lax-Friedrichs one if necessary in order to be oscillation free (Total Variation Diminushing). Various numerical examples illustrate the efficiency of our scheme