The extension of the ideas of multigrid to complex compressible flow calculation is generally not straight-forward, especially when non-embedded grids or volume agglomerations are used in order to work with unstructured grids. In this report, we study a multigrid method for solving second order PDE's on stretched unstructured triangulations. We use the finite volume agglomeration multigrid approach developed for solving the Euler equations. First, we present a method to generate coarse grids by volume agglomeration, allowing a directional semi-coarsening based on the Poisson's equation coefficients. The second order derivatives are approximated at each level by introducing a correction factor adapted to semi-coarsening. Then, we apply this method to solve the Poisson equation and extend it to the 2D turbulent Navier-Stokes equations with a low-Reynolds boundary heatment
