In this study, a heterogeneous flow model is proposed based on a non-overlapping domain decomposition method. The model combines potential flow and incompressible viscous flow. Both flow domains contain a free surface boundary.
The heterogeneous domain decomposition method is formulated following the Dirichlet-Neumann method. Both an implicit scheme and an explicit scheme are proposed. The algebraic form of the implicit scheme is of the same form of the Dirichlet--Neumann method, whereas the explicit scheme can be interpreted as the classical staggered scheme using the splitting of the Dirichlet-Neumann method.
The explicit scheme is implemented based on two numerical solvers, a Boundary element method (BEM) solver for the potential flow model, and a finite element method (FEM) solver for the Navier-Stokes equations (NSE). The implementation based on the two solvers is validated using numerical examples.