求解可压缩Navier-Stokes方程的预处理JFNK方法研究

Preconditioned JFNK method for solving compressible Navier-Stokes equations

为了提高可压缩雷诺平均Navier-Stokes(RANS)方程的求解效率,基于多块对接结构化网格发展了求解RANS方程的Jacobian-Free Newton Krylov(JFNK)方法.JFNK方法将求解非线性方程的非精确Newton法和求解线性方程的Krylov子空间迭代法结合,通过非精确Newton方法中不精确条件控制不同阶段线性方程的求解精度,并利用无矩阵技术求解矩阵与向量的乘积;针对Krylov内迭代收敛停滞的问题,引入LU-SGS方法作为预处理器,降低线性系统的刚性从而大幅度提高了内迭代的计算效率.利用JFNK方法模拟NACA 0012翼型、带襟翼的NLR-7301两段翼与带发动机短舱的DLR-F6翼身组合体的绕流问题,研究不同参数对JFNK方法收敛特性的影响,对比LU-SGS研究JFNK方法的收敛速度,并对JFNK方法求解复杂绕流问题的RANS方程进行确认.结果表明,JFNK方法求解RANS方程具有良好的稳定性,相对于其他时间推进方法,JFNK方法具有更高的计算效率.

To improve the computation efficiency, this article introduces Jacobian-Free Newton Krylov（JFNK） method to solve compressible Reynolds Averaged Navier-Stokes（RANS） equations on multiblock structural mesh. JFNK method combines inexact Newton method for solving nonlinear equations with Krylov Subspace method for solving linear equations, and it introduces inexact condition to control solution accuracy of linear equations, and matrix vector multiplication is computed with a Jacobian free method. To overcome ＂convergence stagnation＂ problem in linear iterations, a LU-SGS based preconditioner is introduced to reduce the condition number of linear system, which accelerates the convergence rate of linear iterations. Flow around NACA 0012 airfoil, NLR-7301 wing with flap and DLR-F6 wing-body-pylon-nacelle configuration is simulated to validate the JFNK method. Results show that preconditioned JFNK method has better stability and higher efficiency compared with other methods.