Weighted Compact Scheme for Shock Capturing
Weighted Compact Scheme for Shock Capturing
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DOI：
10.1080/10618560108970024
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发表时间：
2001-10
影响因子：
1.3
通讯作者：
Li Jiang;H. Shan;Chaoqun Liu
中科院分区：
文献类型：
--
作者：
Li Jiang;H. Shan;Chaoqun Liu
摘要 本文提出了一类新的有限差分格式——加权紧致格式。根据WENO方案的思想，加权紧凑方案是通过将候选模板上的导数近似与适当分配的权重相结合来构造的，以便在出现不连续时实现非振荡特性。应用ENO方案的原函数重构方法得到加权紧致方案的保守形式。这种新方案不仅保留了标准紧凑方案的特点，利用紧凑模板实现了高阶精度和高分辨率，而且能够准确捕获冲击波和不连续性而不会产生振荡。数值例子表明新方案是非常有前途和成功的。
Abstract In this paper a new class of finite difference schemes - the Weighted Compact Schemes are proposed. According to the idea of the WENO schemes, the Weighted Compact Scheme is constructed by a combination of the approximations of derivatives on candidate stencils with properly assigned weights so that the non-oscillatory property is achieve when discontinuities appear. The primitive function reconstruction method of ENO schemes is applied to obtain the conservative form of the Weighted Compact Scheme. This new scheme not only preserves the characteristic of standard compact schemes and achieves high order accuracy and high resolution using a compact stencil, but also can accurately capture shock waves and discontinuities without oscillation. Numerical examples show the new scheme is very promising and successful.