Parallel linear multigrid algorithms for the acceleration of compressible flow calculations Original Research Article

The interest in unstructured meshes for Computational Fluid Dynamics (CFD) applications appears to be increasingly important in the industrial community. Industrial applications require the numerical simulation of complex flows (i.e. the underlying flows exhibit localized high variations of physical quantities) around or within complex geometries. Unstructured meshes are particularly well suited to these kinds of simulation due to their ability in accurately discretizing complex computational domains and, to their flexibility in dynamically refining and derefining, or deforming, in order to match the underlying flow features. Concerning flow solvers, the main question appears to be the lack of efficiency demonstrated by unstructured mesh solvers compared to structured ones. Many efficient methods developed in the structured context are not easily extensible to unstructured meshes and much research work has yet to be done in this direction. During the last ten years, several such works have demonstrated that multigrid principles can yield robust and efficient unstructured mesh solvers (see for example Lallemand et al. , Koobus et al. , Carré , Mavriplis et al. ). In this paper, we describe ongoing research activities at Inria Sophia Antipolis aiming at the construction of efficient and robust unstructured multigrid solvers for complex two-dimensional (2D) and three-dimensional (3D) flow simulations. Both academic and industrial aspects are considered.