间断数值摄动算法及NS方程高精度中心有限体积格式与应用

Computational fluid dynamics (CFD) has been developing rapidly in recent half century. CFD has been applying more and more universally to numerical simulation of fluid flows in the fields of aerospace and aeronautics and so on and its effects become more and more great. A key of CFD is algorithm (or scheme) whose developing trend and studying focus are to construct higher performance schemes which are suitable to unstructured and complewx grids. These new schemes ought to be used in CFD software. The numerical pertubation algorithm presented by the author is an original innovative algorithm. The numerical results given by the upwind perturbation NS schemes computing complex flows are very good. A discontinuous numerical perturbation algorithm was presented by the author in studying NNSF project just finished. Some central finite volume (FV) schemes and central finite difference (FD) schemes for convective diffusion equation were constructed by discontinuous perturbation, theses schemes have excellent properties: higher-order accurate, non-oscillatory, simplicity, calculated amount less, no use limiter, no use artificial viscosity, the central FV schemes use the least cell and aresuitable to unstructured and complex grids. The excellent properties of thses schemes above stated are proved by analyses and calculations of one- and two-dimensional model equations. In this project, the AUSM schemes will be perturbed discontinuously and the aim is to build four higher-order accurate, non-oscillatory central FV schemes for Navier-Stokes equations; this four central FV schemes will be added chemical reaction terms which are perturbed and the aim is to build four higher-order accurate, non-oscillatory central NS's FV schemes which are suitable to chemical reaction flows. Two higher-order accurate, non-oscillatory central FV schemes for Navier-Stokes equations in which the pressure is calculated by SIMPLE method will be constructed. By this ten new schemes calculating complex flows and the corresponding numerical results compared with those of other higher-order accurate schemes. We will make these new schemes high performance practical schemes for Navier-Stokes equations.

近几十年计算流体力学（CFD）飞速发展，它在航天航空等领域的流动模型中应用越来越广泛、作用越来越大，它的一个关键是算法，发展趋势和热点是构造能适应非结构等复杂网格的高性能算法，并被软件所使用。申请人提出的数值摄动算法是原创算法。NS方程的迎风摄动格式计算复杂流动具有很好的表现。在刚结题的基金面上项目研究中，我们又提出间断摄动、构建了对流扩散方程的间断摄动中心有限体积（FV）格式和差分（FD）格式，这些格式精度高绝对稳定，简单，不用限制器不用人工粘性，且得到分析和数值证实。本项目开展NS方程间断摄动研究，间断摄动AUSM类格式建成4类NS方程高精度不振荡中心FV格式，并对它们补充摄动反应项，建成4类反应流NS高精度不振荡中心FV格式；构建压力SIMPLE计算的两类NS高精度不振荡中心FV格式；通过复杂流动计算和与其它高精度格式的比较检验，使这十类格式成为NS高性能实用格式。

近几十年计算流体力学（CFD）飞速发展，它在航天航空等领域的流动模型中应用越来越广泛、作用越来越大，它的一个关键是算法，发展趋势和热点是构造能适应非结构等复杂网格的高性能算法，并被软件所使用。本项目在申请人提出的原创算法-数值摄动算法的基础上，进一步分析了摄动算法的对流占优特性及其对摄动算法的影响；利用摄动算法理论发展了摄动加权基本无振荡（P-WENO）格式，该格式降低了WENO格式对达到收敛精度的必要条件的限制，为发展高性能WENO格式提供了一个有效的途径；发展了含源项对流扩散方程的两种数值摄动差分格式以及化学反应方程的高精度摄动格式，有效避免了源项带来的数值刚性问题；在干扰剪切流理论的基础上，提出干扰剪切流稳定性理论并把它用于改进高雷诺数流动计算方法。数值摄动方法为国内原创方法，数值摄动思想为CFD数值方法的发展研究提供了一条新思路，已得到国内外同行专家学者的关注及初步应用。