New Low-Dissipation Central-Upwind Schemes

In this paper, we develop new second-order low-dissipation central-upwind (LDCU) schemes for hyperbolic systems of conservation laws. Like all of the Godunov-type schemes, the proposed LDCU schemes are developed in three steps: reconstruction, evolution, and projection. A major novelty of our approach is in the projection step, which is based on a subcell resolution and designed to sharper approximate contact waves while ensuring a non-oscillatory property of the projected solution. In order to achieve this goal, we take into account properties of the contact waves. We design the LDCU schemes for both the one- and two-dimensional Euler equations of gas dynamics. The new schemes are tested on a variety of numerical examples. The obtained results clearly demonstrate that the proposed LDCU schemes contain substantially smaller amount of numerical dissipation and achieve higher resolution compared with their existing counterparts.