Parallel multigrid Newton-Krylov algorithms for euler computations on 3D unstructured grids

In this paper, a finite volume solver for the computation of three-dimensional steady flows of inviscid compressible perfect gases is presented. This cell-centered solver is designed on unstructured meshes composed of polyhedral cells with triangular or quadrangular faces; this provides complete flexibility for the grid generation, ranging from structured type meshes to fully tetrahedral meshes. To obtain precise solutions, even on relatively coarse meshes, polynomial reconstructions up to quadratic are performed inside each cell, yielding a third order method if combined with sufficiently accurate face integrations. Steady state solutions of the resulting semi-discretized equations are obtained by means of an Euler implicit pseudo-tune advancing strategy based on Newton's method. ILU-preconditioned matrix-free Krylov-based iterative methods are employed to solve the linear systems arising from the successive linearizations. In order to improve the robustness of the solver, a multigrid preconditioning technique has been implemented. A nonlinear multigrid strategy has also been applied to the outer pseudo-time loop to try to provide a better handling of the nonlinearities of the equations and increase the convergence rate. Parallelism is introduced in the solver by a combination of mesh partitioning and message passing, yielding very satisfactory speedups. The computation of the standard transonic flow around the ONERA M6 airfoil assesses the spatial accuracy, in particular for the quadratic reconstruction. The performances of the parallel Newton-Krylov solver are investigated and the considerable convergence gains yielded by both multigrid approaches are illustrated.