Two Dimensional Compressible Flow Solver for Moving Geometries Using Immersed Boundary Method
2020
RESUME La methode des frontieres immergees (IB) a ete mise en œuvre avec un certain succes pour differentes applications, y compris les geometries mobiles et stationnaires. Les travaux actuels portent sur l’extension de la methode IB au traitement du deplacement des geometries pour les applications a ecoulements compressible. En effet, pour les frontieres mobiles, la mise en œuvre de l’approche IB comprend le changement du type de cellules, solide vers fluide, ce qui complexifie la methodologie car il y a un manque dans l’historique de la solution numerique pour ces cellules. Afin de resoudre a cette problematique, deux approches sont disponibles dans la litterature. La premiere approche repose sur l’extrapolation des variables sur les cellules solides adjacentes (cellules fictives). La deuxieme approche utilise la reconstruction de la solution toujours dans la region fluide. Un autre aspect de l’implementation de la methode IB est la representation correcte d’une partie ou la totalite de la geometrie, en particulier lorsque l’echelle geometrique est inferieure a celle du maillage. Ce probleme a ete identifie et resolu pour les geometries 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.
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