适于可压缩多尺度流动的紧致型激波捕捉格式

摘要

针对可压缩多尺度流动数值模拟特点,研究一种五阶高分辨率紧致型激波捕捉格式——紧致重构加权基本无振荡(CRWENO)格式.该格式利用非线性权系数将低阶紧致格式加权组合以达到高阶精度.在光滑区域蜕化成具有高分辨率的五阶线性紧致格式,在间断附近则能保持计算稳定无振荡.对CRWENO格式、目前广泛使用的加权基本无振荡(WENO)格式及两格式对应的线性格式(即五阶线性迎风格式和五阶紧致格式)进行数值性能研究,评估非线性权系数对格式耗散及频谱特性的影响.使用一维、二维、三维典型算例进行数值试验,探讨线性/非线性、紧致/非紧致格式在可压缩多尺度流动模拟中的优势和不足.结果表明,CRWENO格式在强压缩性流场模拟中能够稳定地捕捉激波,其紧致特性则改善了非线性格式普遍存在的耗散过大、分辨率较差的问题,使其能够清晰捕捉多尺度流动结构.因此,该格式在可压缩多尺度流动模拟中具有较大优势.%Aimed at compressible multiscale flow simulations,a fifth-order high-resolution compact shock capturing scheme,compact-reconstruction weighted essentially non-oscillatory (CRWENO),is studied.Nonlinear weights are used to combine lower-order compact schemes to approximate a higher-order compact scheme.The scheme becomes the fifth-order linear compact scheme in smooth regions,while preserves computational stability across discontinuities.Numerical properties were analyzed for CRWENO and weighted essentially non-oscillatory (WENO) which is widely used these days,as well as the linear schemes that they correspond to,i.e.the fifth-order upwind linear scheme and the fifth-order compact scheme.The impacts of nonlinear weights on dissipation and spectral properties are evaluated.The advancements and drawbacks of linearonlinear and compact/explicit schemes in compressible multiscale flow simulations are discussed by performing 1D,2D and 3D typical numerical tests.It can be concluded that CRWENO scheme can obtain non-oscillatory results near strong discontinuous regions.Its compact characteristic improves the problems of over-dissipation and low resolution exiting in nonlinear schemes and makes it clearly resolve multiscale flow structures.In a word,CRWENO is a proper candidate for compressible multiscale flow simulations.