| A Newton-Krylov solver for the Euler equations that govern the flow of a compressible inviscid flow, with application to flows over aerodynamic configurations, is presented. The Euler equations and a nonlinear artificial dissipation scheme are discretised in space using a node-based finite-volume formulation on arbitrary polygonal unstructured grids. The resulting system of nonlinear algebraic equations is solved using an inexact Newton strategy in which the linear problem arising at each Newton iteration is solved iteratively using the matrix-free GMRES algorithm preconditioned by an approximate Jacobian matrix subjected to an incomplete factorisation and reordering. Implicit Euler local time stepping is applied when solving transonic flows.; The solver is tested with single and multi-element airfoils in the subsonic and transonic flow regimes. Various GMRES tolerances, preconditioner fill-in levels, and pre-conditioned tolerances are investigated. Sets of optimum base parameters are determined. Results show the solver to be competitive with other solvers. Recommendations are made for aspects of the solver that are worthy of further study. |
