Computational algorithm using secondary conservative scheme and JFNK method for nonlinear fluid interaction problems

本文基于二次守恒对流格式和JFNK(Jacobian-Free NewtonKrylov)方法，构造了求解非线性流体相互作用问题的数值方法。具体地，构造了(1)不可压缩流动的非分离数值方法，(2)可压缩流动的二次守恒有限差分格式，(3)移动网格的二次守恒有限差分格式，(4)不可压缩流动的高精度紧致有限差分格式，(5)激波捕捉方法和二次守恒有限差分格式的混合格式，以及(6)湍流边界层流动中非牛顿流体的数值方法。

In this study, numerical methods for nonlinear fluid interaction problems were constructed based on the secondary conservative convection scheme and the JFNK(Jacobian-Free NewtonKrylov) method. Specifically,(1) the nonsegregated numerical method for incompressible flows,(2) the secondary conservative finitedifference scheme for compressible flows,(3) the secondary conservative finitedifference convection scheme for moving grids,(4) the high-order accurate compact finitedifference scheme for incompressible flows,(5) the hybrid scheme of the shock capturing method and the secondary conservative finitedifference scheme, and(6) the numerical method for nonNewtonian fluid in turbulent boundary-layer flow, were constructed.