适用于超声速的一种通量限制型紧致格式

A Limited Flux Compact Scheme Suited to Supersonic Flows

紧致格式因其结构简单、在相同的网格点上能达到比非紧致格式更高的精度以及与谱方法相近的分辨率等优点,日益受到人们的重视。用紧致格式模拟超声速流场的主要问题之一是如何保证高阶紧致格式能光滑地捕捉到流场的各种间断。本文借鉴NND格式的思想,构造出一种总体上具有三阶精度的通量限制型紧致(LFC)格式,并成功地应用于含有激波、滑移面等复杂流动现象的数值模拟。计算结果表明这种格式不仅具有较高的精度和分辨率,而且还保证了在间断附近基本无虚假波动。

Compact scheme with spectral-like resolution has higher accuracy than other schemes on the same grid template, as well as the structure of compact scheme is very simple, so that it has attracted more and more attention. The key problem in the usage of compact scheme is how to smoothly capture discontinuities (such as shocks and contact faces). In order to solve the problems, a third-order Limited Flux Compact (LFC) scheme is constructed. This scheme is similar to non-oscillatory, no free parameter, and dissipative scheme. This scheme is successfully used to simulate shock waves, contact discontinuities in non-viscous flows. This scheme is also used to simulate a two-dimensional viscous flow. Calculation results confirm its high accuracy and high resolutions, good ability in capture shock and no oscillation.