CFD High-order Accurate Scheme JFNK Solver

CFD finite difference method high-order accurate scheme can provide more exact flow field solution than second order accurate shceme, but its computing stencil is very border, and hard to get Jacobian matrix for the LU-SGS method, leading to the fact that the LU-SGS convergence speed is slow. A Jacobian-free Newton-Krylov (JFNK) method was developed to a seventh-order accurate scheme HDCS-E8T7, and a kind of nonlinear preconditoner was applied based on traditional 7 diagonal matrix, which was solved with LU-SGS method. In cylinder steady flow case, JFNK method was better than oringal LU-SGS method, nearly half time was saved.