吉布斯现象
分段
数学
不连续性分类
插值(计算机图形学)
守恒定律
应用数学
模板
非线性系统
多项式的
初值问题
休克(循环)
数学分析
计算机科学
医学
动画
物理
计算机图形学(图像)
计算科学
傅里叶变换
量子力学
内科学
作者
A. Harten,Björn Engquist,Stanley Osher,Sukumar Chakravarthy
标识
DOI:10.1016/0021-9991(87)90031-3
摘要
We continue the construction and the analysis of essentially non-oscillatory shock capturing methods for the approximation of hyperbolic conservation laws. We present an hierarchy of uniformly high-order accurate schemes which generalizes Godunov's scheme and its second-order accurate MUSCL extension to an arbitrary order of accuracy. The design involves an essentially non-oscillatory piecewise polynomial reconstruction of the solution from its cell averages, time evolution through an approximate solution of the resulting initial value problem, and averaging of this approximate solution over each cell. The reconstruction algorithm is derived from a new interpolation technique that, when applied to piecewise smooth data, gives high-order accuracy whenever the function is smooth but avoids a Gibbs phenomenon at discontinuities. Unlike standard finite difference methods this procedure uses an adaptive stencil of grid points and, consequently, the resulting schemes are highly nonlinear.
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