一种通量加权型紧致格式

将通量加权的思想引入到紧致格式中,构造了一个传统方法与紧致格式混合组成的加权型差分格式.利用该格式与二阶TVD格式分别计算了一维方波、组合波问题和一些黎曼问题,如Sod问题和Shu问题,以及一维定常激波问题.计算结果的比较表明加权格式无论在捕捉各种间断,还是在分辨各种复杂波系上,都具有较大的优势,并与精确解非常吻合. 

A flux-weighted compact scheme

With introduction of flux-weighted concept into the compact scheme,a new flux-weighted compact scheme was presented by combining classical scheme and compact scheme.This scheme and a 2nd-order total variation diminishing(TVD) scheme were used to calculate one-dimensional square waves,combine waves and some Riemann problems,such as Sod problem and Shu problem,as well as one-dimensional steady shock.The results show that the new scheme has advantage over the 2nd-order TVD scheme in capturing various discontinuities or resolving various complex waves.The results solved by the new scheme are also highly consistent with exact solutions.