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数值摄动算法及其CFD格式
NUMERICAL PERTURBATION ALGORITHM AND ITS CFD SCHEMES

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高智  
文摘 数值摄动算法将流体动力学效应耦合进NS方程组和对流扩散(CD)方程离散的数学基本格式(MBS),特别是耦合进最简单的一阶迎风和二阶中心格式之中,由此构建成一系列新的摄动格式(PS).构建PS的主要步骤是将MBS中的通量重构为步长的幂级数,利用空间分裂和导出的高阶流体动力学线性关系式,并引入下游不影响上游的对流运动规律,通过消除重构格式修正微分方程的截断误差诸项求出幂级数的待定系数,由此获得非线性PS.PS的项是MBS中对应项与R△x(及λR△x)之简单多项式的乘积,R△x和λ分别是网格Reynolds数和网格CFL数.PS和MBS使用相同结点,简单性彼此相当,但PS精度高,稳定范围大,例如PS包含了许多绝对稳定高阶迎风和中心有限差分(FD)格式和绝对正型有限体积(FV)格式,这些格式对网格Reynolds数的任意值均为不振荡格式.数值摄动算法因此是构建高精度不振荡CFD格式的新方法.PS用于计算不可压缩流,可压缩流,液滴萃取传质,微通道两相流等,均获得良好数值结果或与已有Benchmark解一致的数值结果.已有文献称数值摄动算法为新型高精度方法和高算法,文中也讨论了一些值得进一步研究的课题
其他语种文摘 The numerical perturbation algorithm presented by the author is to couple fluid dynamics effects with mathematical basic schemes(MBS), especially with the most simplest MBS,i.e.the first order upwind and the second order central schemes for the Navier–Stokes(NS) equations and convective diffusion equation. As a result, many new schemes are obtained,i.e.perturbational finite difference scheme(PDS) and perturbational finite volume scheme(PVS).The main steps of constructing PDS and PVS are as follows: the flux and coefficient of convective derivative in MBS are reconstructed as power-series of grid interval;by splitting resultant scheme above and operating the splitted scheme, the high-order fluid mechanics relation is obtained;the variables at upstream and downstream nodes are expanded in Taylor series;by eliminating truncated error terms in the modified differential equation of the reconstructed scheme the undetermined coefficients in the power-series are determined and finally the PDS and PVS are obtained. Formulations of PDS and PVS are product of MBS and numerical perturbation reconstruction functions, that are simple polynomial of R△x(or λR△x), where R△x and λ are grid Reynolds number and grid CFL number, respectively. PDS and PVS and the original MBS utlize the same nodes and are nearly equal in simplicity But PDS and PVS have higher accurate and larger stable-range than MBS.For example, the most simplest and the most important six PDS and PVS for the convection diffusion(CD) equation are : sixth-order accurate upwindfinite-difference PDS, dual perturbation(DP) fourth-and eighth-order accurate central PDS, dual perturbationthird-and fifth-order accurate(interpolation approximation) finite volume(FV) central PVS and sixth orderaccurate upwind PVS. This six schemes are absolute stable or absolute positive and are non-oscillatory schemesfor any values of grid Reynolds number. In one dimensional case, this six schemes are TVD scheme for anyvalues of grid Reynolds number. However, the same order MBS must use multi-nodes and oscillate on coarsegrids. PDS and PVS can not only be directly used to calculate flow, but also act as a basic or starting schemefor reconstructing high resolution scheme by self-adjust numerical dissipation. The above six PDS and PVSand others have already been used to calculate incompressible flows, compressible flows, mass transfer and Marangoni convection in the cases of a falling drop, two phase flows and others, and some excellent numericalresults are achieved. For example,PVS solve lib-driven and buoyancy-driven cavity flows and result in severalnew Benchmark solutions. The numerical perturbation algorithm and corresponding schemes are also called Gao's algorithm and Gao's schemes. Several subjects worthy of further study are discussed. The presentmethod is also suitable for reconstructing MBS of other mathematical physics equations(such as the simplified Boltzmann equation, magnetohydrodynamic equations, KdV-Burgers equation etc.) with coupling dynamics effects
来源 力学进展 ,2010,40(6):607-633 【核心库】
关键词 计算流体力学 ; 数值摄动算法 ; 数学基本格式 ; 摄动差分格式 ; 摄动有限体积格式
地址

中国科学院力学研究所高温气体动力学重点实验室, 中国科学院力学研究所高温气体动力学重点实验室, 北京, 100190

语种 中文
文献类型 研究性论文
ISSN 1000-0992
学科 力学
基金 国家自然科学基金资助项目
文献收藏号 CSCD:4063709

参考文献 共 130 共7页

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引证文献 2

1 高智 用物理黏性构建高阶不振荡对流扩散差分格式 力学学报,2012,44(3):505-512
被引 0 次

2 李启兵 气体动理学格式研究进展 力学进展,2012,42(5):522-537
被引 16

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