捕捉间断的高精度数值方法

为发展适用于捕捉超声速流场中各种间断的高精度算法,将通量限制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通量限制型差分格式.通过在时间方向上利用一阶精度格式计算的一维定常激波,以及在时间方向采用多步Runge-Kutta方法计算的一维非定常激波管问题上的数值试验与二阶精度的TVD格式所计算的结果比较,表明新方法比二阶精度方法在间断的捕捉上具有明显的优势.通过新方法的计算结果与精确解的比较,表明新方法的准度也是非常令人满意的.

Study of higher order accuracy algorithm of capturing discontinuity

For developing a higher order accuracy algorithm applying to capturing various discontinuities in supersonic flow, in the process of constructing compact finite difference scheme, the ideal of fluxes limited is utilized. A new scheme mixed with classical scheme and compact scheme is presented. A first-order accuracy scheme for temporal discretization is used to compute one dimension steady shock and a multistage Runge-Kutta time stepping scheme is used to solve Sod problem. The present results were compared with those results computed by the 2nd-order TVD scheme. It showed that the new scheme provides a significant improvement over the 2nd-order TVD scheme in capturing shock. The present results are in good agreement with accurate solutions.