Implementation of semi-discrete, non-staggered central schemes in a colocated, polyhedral, finite volume framework, for high-speed viscous flows
Implementation of semi-discrete, non-staggered central schemes in a colocated, polyhedral, finite volume framework, for high-speed viscous flows
复制标题
DOI：
10.1002/fld.2069
复制
发表时间：
2010-05-10
影响因子：
1.8
通讯作者：
Reese, Jason M.
中科院分区：
文献类型：
--
作者：
Greenshields, Christopher J.;Weller, Henry G.;Reese, Jason M.
我们描述了用于模拟高速流的计算流体动力学求解器的实现。它包含使用半混凝土的，非stagger的中央方案的有限体积（FV）离散化，用于在具有任意面部数量的多面体细胞网的网状细胞上规定的共线变量。我们详细描述了求解器，解释了面部插值受到限制的变量的选择，限制器的选择以及一种限制独立于坐标系的向量场插值的方法。 Navier Stokes方程中的动量和能量传输的解使用操作员分解方法：首先，我们解决了保守变量对流的明确预测器方程，然后求解一个隐式纠正方程来扩散原始变量。我们的求解器对四组数据进行了验证：（1）一维冲击管情况的分析解决方案； （2）在向前的步骤上的二维，瞬态，超音速流的数值解； （3）从圆形喷嘴中对超音速射流的干涉图密度测量； （4）在25度-55度的双孔中高超音速流的压力和传热测量。我们的结果表明，Kurganov，Noelle和Petrova（Siam J.Sci。Comput。2001; 23：707-740）的中央风方方案具有先前发表的最佳方法（例如，分段抛物线抛物线方法，Roe solver with van Leerer）具有竞争力限制）并且它本质上是简单的，并且非常适合于共归结的多面体FV框架。版权所有2009 John Wiley＆Sons，Ltd。
We describe the implementation of a computational fluid dynamics solver for the simulation of high-speed flows. It comprises a finite volume (FV) discretization using semi-discrete, non-staggered central schemes for colocated variables prescribed on a mesh of polyhedral cells that have an arbitrary number of faces. We describe the solver in detail, explaining the choice of variables whose face interpolation is limited, the choice of limiter, and a method for limiting the interpolation of a vector field that is independent of the coordinate system. The solution of momentum and energy transport in the Navier Stokes equations uses an operator-splitting approach: first, we solve an explicit predictor equation for the convection of conserved variables, then an implicit corrector equation for the diffusion of primitive variables. Our solver is validated against four sets of data: (1) an analytical solution of the one-dimensional shock tube case; (2) a numerical solution of two dimensional, transient, supersonic flow over a forward-facing step; (3) interferogram density measurements of a supersonic jet from a circular nozzle; and (4) pressure and heat transfer measurements in hypersonic flow over a 25 degrees-55 degrees biconic. Our results indicate that the central-upwind scheme of Kurganov, Noelle and Petrova (SIAM J. Sci. Comput. 2001; 23:707-740) is competitive with the best methods previously published (e.g. piecewise parabolic method, Roe solver with van Leer limiting) and that it is inherently simple and well suited to a colocated, polyhedral FV framework. Copyright 2009 John Wiley & Sons, Ltd.