Fast unsteady flow computations with a Jacobian-free Newton–Krylov algorithm

Despite the advances in computer power and numerical algorithms over the last decades, solutions to unsteady flow problems remain computing time intensive. Especially for large Reynolds number flows, nonlinear multigrid, which is commonly used to solve the nonlinear systems of equations, converges slowly. The stiffness induced by the large aspect ratio cells and turbulence is not tackled well by this solution method.In previous work we showed that a Jacobian-free Newton–Krylov (jfnk) algorithm, preconditioned with an approximate factorization of the Jacobian that approximately matches the target residual operator, enables a speed up of a factor of 10 compared to standard nonlinear multigrid for two-dimensional, large Reynolds number, unsteady flow computations.The goal of this paper is to demonstrate that the jfnk algorithm is also suited to tackle the stiffness induced by the maximum aspect ratio, the grid density, the physical time step and the Reynolds number. Compared to standard nonlinear multigrid, speed ups up to a factor of 25 are achieved.