摘要
将Choi-Merkle矩阵预处理方法与LU-SGS隐式方法、双时间法以及多重网格方法结合,发展适用于绕飞行器定常和非定常粘性流动的高效隐式预处理计算方法和程序.介绍一种针对定常和非定常流动的LU-SGS隐式预处理方法的统一表述方法.在不改变流动解的前提下,对Navier-Stokes方程的伪时间导数项实施Choi-Merkle矩阵预处理,从而改善可压缩控制方程在低速情况下的系统刚性,使基于LU-SGS时间推进格式的数值模拟方法同时适用于从极低马赫数到可压缩范围内的数值模拟.对Jameson中心格式的人工粘性进行相应的修改,以提高低速流动的计算精度.翼型、机翼以及翼身组合体绕流的数值模拟研究表明,隐式预处理方法获得了很高的计算效率,可使马赫数0.1左右的低速流动计算时间减少50%以上;通过对现有可压缩计算程序进行小量改动,便可使其均匀覆盖整个低速流动范围,提高CFD程序在飞行器绕流数值模拟中的实用性.
An LU-SGS based Choi-Merkle matrix preconditioning method is implemented within the framework of dual-time stepping and geometric muhigrid method. An efficient method for steady and unsteady flows past aircraft configurations with Mach numbers from incompressible to transonic regime is developed. LU-SGS time stepping method is modified according to the preconditioned system. An efficient and robust splitting method for Jacobian matrix is presented. In simulation of viscous flows past NACA0012 airfoil ONERA M6 wing and DLR F4 wing/body configuration, the method obtains nearly Mach number-independent convergence at low-Mach numbers and improves efi%iency slightly for transonic flows. Compared with Runge-Kutta based preconditioning method, LU-SGS based preconditioning method is more efficient. In simulation of unsteady viscous flow past an oscillating NACA 0012 airfoil convergence of sub iteration of dual time stepping is improved shghtly.
出处
《计算物理》
EI
CSCD
北大核心
2009年第5期679-684,共6页
Chinese Journal of Computational Physics
