The LS-STAG immersed boundary/cut-cell method for non-Newtonian flows in 3D extruded geometries

International audienceThe LS-STAG method is an immersed boundary/cut-cell method for viscous incompressible flows based on the staggered MAC arrangement for Cartesian grids, where the irregular boundary is sharply represented by its level-set function, results in a significant gain in computer resources (wall time, memory usage) compared to commercial body-fitted CFD codes. The 2D version of LS-STAG method is now well-established (Y. this paper presents its extension to 3D geometries with translational symmetry in the z direction (hereinafter called 3D extruded configurations). This intermediate step towards the fully 3D implementation can be applied to a wide variety of canonical flows and will be regarded as the keystone for the full 3D solver, since both discretization and implementation issues on distributed memory machines are tackled at this stage of development. The LS-STAG method is then applied to various Newtonian and non-Newtonian flows in 3D extruded geometries (axisymmetric pipe, circular cylinder, duct with an abrupt expansion) for which benchmark results and experimental data are available. The purpose of these investigations are (a) to investigate the formal order of accuracy of the LS-STAG method, (b) to asses the versatility of method for flow applications at various regimes (Newtonian and shear-thinning fluids, steady and unsteady laminar to turbulent flows) (c) to compare its performance with well-established numerical methods (body-fitted and immersed boundary methods)

Two Dimensional Compressible Flow Solver for Moving Geometries Using Immersed Boundary Method

RÉSUMÉ La méthode des frontières immergées (IB) a été mise en œuvre avec un certain succès pour différentes applications, y compris les géométries mobiles et stationnaires. Les travaux actuels portent sur l’extension de la méthode IB au traitement du déplacement des géométries pour les applications à écoulements compressible. En effet, pour les frontières mobiles, la mise en œuvre de l’approche IB comprend le changement du type de cellules, solide vers fluide, ce qui complexifie la méthodologie car il y a un manque dans l’historique de la solution numérique pour ces cellules. Afin de résoudre à cette problématique, deux approches sont disponibles dans la littérature. La première approche repose sur l’extrapolation des variables sur les cellules solides adjacentes (cellules fictives). La deuxième approche utilise la reconstruction de la solution toujours dans la région fluide. Un autre aspect de l’implémentation de la méthode IB est la représentation correcte d’une partie ou la totalité de la géométrie, en particulier lorsque l’échelle géométrique est inférieure à celle du maillage. Ce problème a été identifié et résolu pour les géométries stationnaires.----------ABSTRACT Immersed Boundary (IB) methods have been successfully implemented for different appli- cations including moving as well as stationary geometries. Present work focuses on the implementation of IB method for moving geometries for compressible flow cases. IB imple- mentation for moving boundaries includes the conversion of solid cells to fluid cells, which makes the problem a challenging one because of the abnormal values of the derivatives of pressure and velocity for the cells being converted. In order to solve this problem, mainly two different groups of methods are available. The first group of methods relies on extrapolating the variables on the adjacent solid cells(Ghost Cells) and the second group deals only with the interpolation in the fluid region. Another aspect of IB method implementation is the proper identification of the geometry or a part of the geometry, especially when the size of the geometry is smaller than the mesh size. This problem has been identified and solved for stationary geometries