Steady relaxation methods for unstructured multigrid Euler and Navier-Stokes solutions

This study focuses on the unstructured-mesh multi-grid computation of two-dimensional, steady, transonic hows governed by the Euler or Navier-Stokes equations (in the laminar, low-Reynolds number regime). The central question is the construction of an algorithm of truly O(N) complexity for second-order accurate schemes. This is achieved either by the ''first-order/second-order'' Defect-Correction process, or directly by a fully ''second-order'' approach. Relations between levels are controlled by a coarsening method introduced by Guillard. This work attempts to follow the available theoretical facts to build several strategies that are then evaluated for a set of airfoil flows.