CFD high-order accurate scheme Jacobian-Free Newton Krylov method

•We applied JFNK method to CFD high-order accurate scheme.•We formed a nonlinear type of preconditioner.•A high efficiency precondition matrix for high-order accurate scheme was formed.•Test cases shown that wall time was saved half with JFNK method. High-order accurate scheme for Computational Fluid Dynamics (CFD) finite difference method can provide more exact flow field solution than second order accurate scheme, but it is hard to get Jacobian matrix for lower–upper symmetric Gauss–Seidel (LU-SGS) method because of its complicated computing stencil, which lead to the poor convergence speed of LU-SGS. A Jacobian-Free Newton–Krylov (JFNK) method of high-order accurate scheme was developed, and a nonlinear type of preconditioner was applied based on traditional 7 diagonals matrix, which was solved with LU-SGS method. In cylinder steady flow case, JFNK method was better than original LU-SGS method, nearly one half wall time was saved.