High Order ENO and WENO Schemes for Computational Fluid Dynamics

In these lectures we present the basic ideas and recent development in the construction, analysis, and implementation of ENO (Essentially Non-Oscillatory) and WENO (Weighted Essentially Non-Oscillatory) schemes and their applications to computational fluid dynamics. ENO and WENO schemes are high order accurate finite difference or finite volume schemes designed for problems with piecewise smooth solutions containing discontinuities. The key idea lies at the approximation level, where a nonlinear adaptive procedure is used to automatically choose the locally smoothest stencil, hence avoiding crossing discontinuities in the interpolation procedure as much as possible. ENO and WENO schemes have been quite successful in computational fluid dynamics and other applications, especially for problems containing both shocks and complicated smooth solution structures, such as compressible turbulence simulations and aeroacoustics.