  We develop a combined field formulation for the fluid structure (FS)
interaction problem. The unknowns are (u;p;v), being the fluid velocity, fluid
pressure and solid velocity. This combined field formulation uses Arbitrary
Lagrangian Eulerian (ALE) description for the fluid and Lagrangian description
for the solid. It automatically enforces the simultaneous continuities of both
velocity and traction along the FS interface. We present a first order in time
fully discrete scheme when the flow is incompressible Navier-Stokes and when
the solid is elastic. The interface position is determined by first order
extrapolation so that the generation of the fluid mesh and the computation of
(u;p;v) are decoupled. This explicit interface advancing enables us to save
half of the unknowns comparing with traditional monolithic schemes. When the
solid has convex strain energy (e.g. linear elastic), we prove that the total
energy of the fluid and the solid at time t^{n} is bounded by the total energy
at time t^{n-1}. Like in the continuous case, the fluid mesh velocity which is
used in ALE description does not enter into the stability bound. Surprisingly,
the nonlinear convection term in the Navier-Stokes equations plays a crucial
role to stabilize the scheme and the stability result does not apply to Stokes
flow. As the nonlinear convection term is treated semi-implicitly, in each time
step, we only need to solve a linear system (and only once) which involves
merely (u;p;v) if the solid is linear elastic. Two numerical tests including
the benchmark test of Navier-Stokes flow past a Saint Venant-Kirchhoff elastic
bar are performed. In addition to the stability, we also confirm the first
order temporal accuracy of our explicit interface advancing scheme.
