UNIFORMLY HIGH-ORDER ACCURATE ESSENTIALLY NONOSCILLATORY SCHEMES .3.
UNIFORMLY HIGH-ORDER ACCURATE ESSENTIALLY NONOSCILLATORY SCHEMES .3.
复制标题
DOI：
10.1016/0021-9991(87)90031-3
复制
发表时间：
1987-08-01
影响因子：
4.1
通讯作者：
CHAKRAVARTHY, SR
中科院分区：
文献类型：
--
作者：
HARTEN, A;ENGQUIST, B;CHAKRAVARTHY, SR
我们继续构造和分析近似双曲型守恒律的基本非振荡激波捕捉方法。我们提出了一个一致高阶精度格式，它将Godunov格式及其二阶精度MUSCL推广推广到任意精度阶。该设计涉及从其单元平均值重建解的基本无振荡分段多项式，通过所产生的初值问题的近似解的时间演变，以及在每个单元上平均该近似解。重建算法源于一种新的内插技术，当应用于分段光滑数据时，当函数光滑时，可提供高阶精度，但避免了在不连续处的Gibbs现象。与标准的有限差分方法不同，该方法使用自适应网格点模板，因此，所得到的格式是高度非线性的。
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.