Survey and Recent Development of WENO Schemes

WENO (weighted essentially non-oscillatory) schemes are high order finite difference and finite volume schemes for solving hyperbolic conservation laws with discontinuous solutions. They are designed with nonlinear weights aiming at maintaining both high order accuracy and non-oscillatory shock transitions and are especially suitable for problems containing both discontinuities and complex solution features, such as compressible turbulence and instabilities.
In this talk I will first give a survey of WENO schemes, followed by a description of a few recent developments, including the finite difference WENO schemes on multiple domains (joint work with Kurt Sebastian) and resolution of high order WENO schemes for complicated flow structures (joint work with Jing Shi, Yongtao Zhang and Ye Zhou).