Uniformly High Order Accurate Essentially Non-oscillatory Schemes, III

被引：6

作者：

Harten, Ami ^{[1
,2
]}

Engquist, Bjorn ^{[1
]}

Osher, Stanley ^{[1
]}

Chakravarthy, Sukumar R. ^{[3
]}

机构：

[1] Department of Mathematics, Univ. of California at Los Angeles, Los Angeles, CA 90024, United States

[2] School of Mathematical Sciences, Tel-Aviv University, Tel Aviv, Israel

[3] Rockwell Science Center, Thousand Oaks, CA, United States

来源：

Journal of Computational Physics | 1997年 / 131卷 / 01期

基金：

美国国家科学基金会; 美国国家航空航天局;

关键词：

Finite difference method - Polynomials;

D O I：

暂无

中图分类号：

学科分类号：

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. © 1997 Academic Press.

引用

页码：3 / 47