A Newton-Krylov solver for the Navier-Stokes equations on unstructured grids

grantor: University of TorontoA two-dimensional Newton-Krylov solver for compressible viscous flows has been developed. The Navier-Stokes equations are discretised in space using a finite-volume formulation on arbitrary polygonal meshes. Nonlinear scalar artificial dissipation is added for numerical stability. Newton's method is used to solve the discrete nonlinear algebraic equations, while an ILU-preconditioned, matrix-free GMRES method solves the resulting linear systems. RCM reordering is used to reduce bandwidth, and local implicit-Euler time stepping promotes robustness during start-up. The solver has been verified for a variety of laminar test cases. Optimal parameters have been obtained considering both speed and memory requirements. Extension to turbulent flows is discussed.M.A.Sc