ABSTRACT A typical weighted compact nonlinear scheme (WCNS) uses a convex combination of several low-order polynomials approximated over selected candidate stencils of the same width, achieving non-oscillatory interpolation near discontinuities and high-order accuracy for smooth solutions. In this paper, we present a new multi-resolution fifth-order WCNS by making use of the information of polynomials on three nested central spatial sub-stencils having first-, third- and fifth-order accuracy, respectively. The new scheme is capable of obtaining high-order spatial interpolation in smooth regions, and it is characterised by the feature of gradually degrading from fifth-order down to first-order accuracy as large stencils deemed to be crossing strong discontinuities. The advantages of the present scheme include the superior resolution for high-wavenumber fluctuations and the flexibility of implementing different numerical flux functions.

中文翻译：

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双曲守恒定律的多分辨率加权紧致非线性方案

摘要 典型的加权紧凑非线性方案 (WCNS) 使用几个低阶多项式的凸组合，这些低阶多项式在相同宽度的选定候选模板上近似，实现了不连续附近的非振荡插值和平滑解的高阶精度。在本文中，我们利用分别具有一阶、三阶和五阶精度的三个嵌套中心空间子模板上的多项式信息，提出了一种新的多分辨率五阶 WCNS。新方案能够在平滑区域获得高阶空间插值，其特点是大模板被认为跨越强不连续性，从五阶精度逐渐下降到一阶精度。