ENO(Essentially Non-Oscillatory)方法是一类求偏微分方程数值解的高分辨率方法(High-resolution scheme),由Harten, Engquist, Osher 和 Chakravarthy在1987年提出. 1994年，Liu, Chan 和 Osher 研究了 weighted version of ENO(WENO). In 1996, Guang-Sh 与 Chi-Wang Shu 发展了新的WENO方法并命名为WENO-JS。
有限体积法(FVM)简介
Given cell average $\bar{u}j$ , compute point values $u{j+\frac{1}{2}}^-$ .
ENO推导
ENO: adaptively choose stencil to reduce oscillation. Given the cell average Find a $k$-th order accurate estimates for the values of $u(x)$ at the cell boundaries. Particularly the basis of this approximation is formed by polynomials of degree at most k − 1.
1st order
$u_{j+\frac{1}{2}}^- = \bar{u}_j$: 直接用平均值代替点值。
2nd order
在stencil $[\bar{u}{j-1},\bar{u}{j}]$ 或 $[\bar{u}{j},\bar{u}{j+1}]$ 上计算 $u_{j+\frac{1}{2}}^-$ : \(u^-_{j+\frac{1}{2}} = ss\)
