An efficient heterogeneous flow model that combines incompressible viscous flow and potential flow(PF)(both) with free-surface boundaries for fluid–structure interaction(FSI) problems was developed and solved numerically. In the model, the near field(viscous) fluid subdomain of the FSI simulation is described by the Navier–Stokes equations(NSE), whereas the far field(inviscid) subdomain is described by PF. This method is particularly suitable for modeling a large fluid domain while avoid solving the NSE at the far field, where the inviscid flow assumption is appropriate and adopting a simplified(e.g., PF) flow description reduces computing cost. Numerically, the NSE are solved using a FEM, and the PF is solved using a BEM. Free surface tracking is achieved through a hybrid level set method for the NSE and the mixed Eulerian–Lagrangian method for the PF. The coupling is based on a non-overlapping DD method similar to the Dirichlet–Neumann method. At the interface between the two flow model subdomains, velocity and pressure are matched to ensure continuity of the corresponding variables at the common boundary. In this framework of the heterogeneous DD method, an explicit scheme is developed and implemented. The relation between this scheme and the classical Dirichlet–Neumann method for a homogeneous problem is revealed. Numerical examples demonstrating the capability of the method to model nonlinear wave phenomena and FSI problems with flexible structures are presented. Copyright © 2013 John Wiley & Sons, Ltd.