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,...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.展开更多
We have introduced a fully second order IMplicit/EXplicit(IMEX)time integration technique for solving the compressible Euler equations plus nonlinear heat conduction problems(also known as the radiation hydrodynamics ...We have introduced a fully second order IMplicit/EXplicit(IMEX)time integration technique for solving the compressible Euler equations plus nonlinear heat conduction problems(also known as the radiation hydrodynamics problems)in Kadioglu et al.,J.Comp.Physics[22,24].In this paper,we study the implications when this method is applied to the incompressible Navier-Stokes(N-S)equations.The IMEX method is applied to the incompressible flow equations in the following manner.The hyperbolic terms of the flow equations are solved explicitly exploiting the well understood explicit schemes.On the other hand,an implicit strategy is employed for the non-hyperbolic terms.The explicit part is embedded in the implicit step in such a way that it is solved as part of the non-linear function evaluation within the framework of the Jacobian-Free Newton Krylov(JFNK)method[8,29,31].This is done to obtain a self-consistent implementation of the IMEX method that eliminates the potential order reduction in time accuracy due to the specific operator separation.We employ a simple yet quite effective fractional step projection methodology(similar to those in[11,19,21,30])as our preconditioner inside the JFNK solver.We present results from several test calculations.For each test,we show second order time convergence.Finally,we present a study for the algorithm performance of the JFNK solver with the new projection method based preconditioner.展开更多
文摘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.
基金by a contractor of the U.S.Government under Contract No.DEAC07-05ID14517.
文摘We have introduced a fully second order IMplicit/EXplicit(IMEX)time integration technique for solving the compressible Euler equations plus nonlinear heat conduction problems(also known as the radiation hydrodynamics problems)in Kadioglu et al.,J.Comp.Physics[22,24].In this paper,we study the implications when this method is applied to the incompressible Navier-Stokes(N-S)equations.The IMEX method is applied to the incompressible flow equations in the following manner.The hyperbolic terms of the flow equations are solved explicitly exploiting the well understood explicit schemes.On the other hand,an implicit strategy is employed for the non-hyperbolic terms.The explicit part is embedded in the implicit step in such a way that it is solved as part of the non-linear function evaluation within the framework of the Jacobian-Free Newton Krylov(JFNK)method[8,29,31].This is done to obtain a self-consistent implementation of the IMEX method that eliminates the potential order reduction in time accuracy due to the specific operator separation.We employ a simple yet quite effective fractional step projection methodology(similar to those in[11,19,21,30])as our preconditioner inside the JFNK solver.We present results from several test calculations.For each test,we show second order time convergence.Finally,we present a study for the algorithm performance of the JFNK solver with the new projection method based preconditioner.
