Assignment 0: Describe a Parallel Application

Weighted essentially non-oscillatory (WENO) schemes are effective numerical methods to compute flows having shocks and steep gradients. WENO schemes are based on the successful essentially non-oscillatory (ENO) schemes introduced in [9] and [10]. The initial WENO scheme is constructed in [6], and further research in WENO can be found in papers such as [2], [4] and [5]. Both ENO and WENO schemes use adaptive stencils in the reconstruction procedure based on the local smoothness of the numerical solution to automatically achieve high order accuracy and non-oscillatory property near discontinuities. Instead of choosing the optimal stencil candidate to pick an interpolating polynomial in the reconstruction procedure, WENO schemes use a convex combination of all candidates to achieve the essentially non-oscillatory property. The coefficient of each candidate is a nonlinear weight which depends on the local smoothness of the numerical solution based on the stencil.