A SEVENTH ORDER CENTRAL HWENO SCHEME ON STRAGGERED MESHES FOR CONSERVATION LAWS

In this paper, we present a central seventh order Hermite essentially non oscillatory (HWENO) scheme by extending the fifth order HWENO scheme [(1)] which is formulated on staggered meshes. It consists of seventh order HWENO reconstruction in space and fourth order Lax-Wendroff (L-W) for time. To compute the ideal weights TAO et al. [(1)] used the procedure presented in [(2)] which suffers from two drawbacks. Firstly, the weights may become negative and therefore WENO procedures cannot be applied directly to obtain a monotone scheme, Tao used a splitting technique to deal with this problem. Secondly, the procedure to compute these weights and the treating technique of the negativity is very complicated and very difficult to implement. To avoid these problems, we used the approach presented in [(3)] which depends on the reconstruction of a central polynomial. The resulting ideal weights are symmetric. The advantages of our method are: it lies upon central and local HWENO schemes, the choice of the ideal weights has no effect on the accuracy of the discretization, it is more accurate, easy to implement, more compact, computationally efficient and it requires neither flux splitting nor the use of numerical flux. A variety of numerical tests are presented to validate the performance of the proposed scheme.