Open AccessAn immersed boundary/level-set method for incompressible viscous flows in complex geometries with good conservation properties
Author(s) -
Yoann Cheny,
Olivier Botella
Publication year - 2009
Publication title -
european journal of computational mechanics
Language(s) - English
Resource type - Journals
eISSN - 2642-2085
pISSN - 2642-2050
DOI - 10.13052/ejcm.18.561-587
Subject(s) - immersed boundary method , discretization , boundary (topology) , robustness (evolution) , grid , mathematics , level set method , regular grid , cartesian coordinate system , computation , compressibility , boundary value problem , benchmark (surveying) , geometry , mathematical optimization , mathematical analysis , computer science , mechanics , physics , algorithm , geology , biochemistry , chemistry , geodesy , segmentation , artificial intelligence , image segmentation , gene
This paper concerns the development of a new Cartesian grid / immersed boundary (IB) method for the computation of incompressible viscous flows in irregular geometries. In IB methods, the computational grid is not aligned with the irregular boundary, and of upmost importance for accuracy and stability is the discretization in cells which are “cut" by the boundary. In this paper, we present an IB method (the LS-STAG method) based on the Cartesian MAC method where the irregular boundary is represented by its level-set function. This implicit representation of the immersed boundary enables us to discretize efficiently the fluxes in the cut-cells by imposing the strict conservation of total kinetic energy at the discrete level. The accuracy and robustness of our method are assessed on benchmark flows.