In this work, a heterogeneous flow model is proposed based
on the non--overlapping domain decomposition method. The
model combines potential flow and incompressible
viscous flow. Both models contain free surface boundary.
The heterogeneous domain decomposition method is formulated
following the Dirichlet--Neumann method. Both the implicit
scheme and 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. Boundary element method~(BEM) is used as a solver
in the potential flow domain, and finite element method~(FEM)
is used to solve Navier--Stokes equations~(NSE) in the other domain. The
implementation based on these two solvers is validated
using numerical examples.