高阶紧致格式分区并行算法

Zone decomposition parallel algorithm of high order compact scheme

针对超声速多尺度复杂流动问题,发展了一种高精度并行算法。计算格式采用五阶迎风紧致格式,用特征型通量限制方法抑制非物理振荡。在对接边界处采用五阶WENO格式,以保证整个计算域内计算精度一致。通过网格分区和数据交换,在MPI平台实现了并行计算。通过超声速算例对算法进行了验证,并对并行效率和加速比进行了分析。最后,将算法应用于超声速转捩、湍流问题的数值模拟。计算结果表明,提出的算法具有较高的精度和分辨率,对接边界光滑连续,并且并行效率较高,在高超声速湍流流动数值模拟中取得了较好的应用效果。

A high order parallel algorithm was developed for the simulation of supersonic complex multi- scale flows. The fifth-order upwind compact scheme based on finite volume method was utilized, and the characteristic limiter was used to prevent non-physical oscillations across discontinuity. The fifth WENO schemes were used in adjoining boundaries to achieve consistent precision order in the whole computing domain. Using zone decomposition method and message communicating interfaces, parallel calculation is carried out on MPI platform. The capability of the algorithm is demonstrated by solving supersonic test cases, and the parallel efficiency and speedup are analyzed. Then the algorithm is used for the simulation of supersonic transition and turbulence. The computed results reveal that the developed algorithm has the properties of high-order accuracy and high resolution. Besides, the computed flow fields are conti- nuous in adjoining boundary, and the parallel computing efficiency is acceptable. The algorithm achieves admirable effect in the numerical simulation of supersonic turbulence.