The LS-STAG method is an immersed boundary 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. The level-set function enables us to compute efficiently all relevant geometry parameters of the so-called “cut-cells”, i.e. the cells that are cut by the immersed boundary, reducing thus the bookkeeping associated to the handling of complex geometries. One of the main features of the LS-STAG method is the use of a consistent and unified discretization of the flow equations in both Cartesian and cut-cells, which has been obtained by enforcing the strict conservation of global invariants of the flow such as total mass, momentum and kinetic energy in the whole fluid domain. After a short discussion on the salient features of the LS-STAG method, we will present one of its most recent application: The computation of viscoelastic flows governed by the Oldroyd-B constitutive equation.

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