Application of Jacobian-Free Newton-Krylov method in RANS simulation of turbomachinery

The CFD solver based on the Reynolds averaged stress (RANS) equation remains the main tool for aerodynamic analysis of turbomachinery at present. In order to minimize manual intervention in numerical simulation, the RANS solver needs to have good convergence and robustness. A fast implicit Jacobian-Free Newton-Krylov finite volume method has been developed for steady-state simulation of turbomachinery based on multi-block structure mesh. Based on the generalized residual minimization (GMRES) method, a matrix free solution for large-scale linear sparse systems was implemented, which avoids expensive and complex explicitly assembly of high-order Jacobian matrices. To reduce the difficulty of solving linear systems, a low order Jacobian matrix assembled by graph coloring and finite difference method is adopted to precondition the linear system. In nonlinear iteration, globalization strategy is applied to update the flow solution, improving convergence efficiency and robustness. The approximate Jacobian matrix is used for iterative calculation in the initial calculation to obtain sufficiently accurate flow field linearization, and then switched to Newton iterative method to achieve the goal of nonlinear convergence. Finally, some classic cases were used to verify the accuracy and robustness of the simulation.