  We present a projection-based numerical integration technique to deal with
embedded interface in finite element (FE) framework. The element cut by an
embedded interface is denoted as a cut cell. We recognize elemental matrices of
a cut cell can be reconstructed from the elemental matrices of its sub-divided
cells, via projection at matrix level. These sub-divided cells are termed as
integration cells. The proposed technique possesses following characteristics
(1) no change in FE formulation and quadrature rule; (2) consistency with the
derivation of FE formulation in variational principle. It can be considered as
a re-projection of the residuals of equation system in the test function space
or a reduced-order modeling (ROM) technique. These characteristics
significantly improves its scalability, easy-to-implementation and robustness
to deal with problems involving embedded discontinuities in FE framework.
Numerical examples, e.g., vortex-induced vibration (VIV), rotation, free fall
and rigid-body contact in which the proposed technique is implemented to
integrate the variational form of Navier-Stokes equations in cut cells, are
presented.
