Recent Development and Applications of WENO Schemes

This paper is a summary of the authors talk given in the Third AFOSR International Conference on DNSLES TAICDL. This paper briefly presents the general ideas of high order accurate weighted essentially non-oscillatory WENO schemes, and describe the similarities and differences of the two classes of WENO schemes finite volume schemes and finite difference schemes. We also briefly mention two recent developments of WENO schemes, namely a technique to treat negative linear weights and a class of high order central WENO schemes.