基于保色散关系的迎风WENO格式的研究

A New Upwind-WENO Difference Scheme Based on Dissipation-Relation-Preserving(DRP)

W ENO(W eighted E ssentially N on-O scillatory)格式能够高分辨率地捕捉诸如激波等间断,而保色散关系(D issipation-R elation-P reserv ing,DRP)格式适宜于处理高频波传播问题。计算气动声学(Com putational-A eroacoustics,CAA)领域有大量的既有高频波传播又带有激波的问题,结合W ENO格式和DRP格式的优点基于保色散关系构造出优化的迎风W ENO格式。数值实验中比较该格式捕捉波数的能力和精度,显示处理CAA基本问题具有高精度、高分辨率的特点。

Purpose. There exists a difference scheme based on DRPEzJ. We now present a new upwind- WENO （Weighted Essentially Non-Oscillatory） difference scheme based on DRP that, we believe, can offer numerical results good in precision and high-resolution. In the full paper, we explain our new scheme in much detail, here we only give a briefing. WENO schemes are designed for high-resolution of discontinuities such as shock waves, while DRP schemes are designed for optimization of short waves in the wave number space. We seek to unite the advantages of WENO and DRP schemes through the development of optimized upwind-WENO schemes to tackle shocks whose waves are high in frequency relative to the grid spacing. Optimized upwind WENO scheme is obtained by minimizing the error in the wave number space based on dissipation and dispersion relations. Finally we give three figures showing results of numerical tests of our new upwind-WENO difference scheme based on DRP for representative 1D computational aeroracoustic problems. We now explain briefly only the results concerning the very important shock and sine wave interaction. Our new scheme can capture correctly discontinuity and short wave with high-resolution, and obtain quite correct phase and amplitude positions. In short, these numerical results show preliminarily the good precision and high-resolution of our new scheme.