Numerical Scheme with ENO Reconstruction Satisfying Two Conversation Laws

In recent years, Mao and his co-workers developed a class of finite-volume schemes for evolution partial differential equations. The schemes have more than one numerical entities. Numerical experiments show that these schemes have good structure-preserving property in long-time numerical simulations. In this paper, we propose a scheme which combine the idea of paper and that of the ENO scheme. Our scheme satisfies two conversation laws, and in every cell the polynomial is reconstructed with ENO´s moving stencil. Numerical experiments show that our scheme is robust in long-time behaviors.