ABSTRACT
This paper presents a novel space–time upwind cell-vertex scheme (STU-CVS) for conservation laws. The new scheme is inspired by the revolutional space–time conservation element/solution element (CE/SE) method that utilizes a staggered space–time mesh to enforce the space–time flux conservation. It will be shown that the new scheme is independent of the underlying mesh, and the implementation of the new scheme becomes easier and more clear compared with the original CE/SE method. We also explore the inherent upwind nature of the new scheme as well as the CE/SE method. The inherent upwind nature eliminates the need of using Riemann solvers for advection-dominant problems. The numerical dissipation of the new scheme as well as the CE/SE method is small. Finally, we provide some preliminary numerical results to demonstrate the performance of the new scheme.