  We present the Fully cOUpled loCAl model of sUperfLuid Turbulence (FOUCAULT)
that describes the dynamics of finite temperature superfluids. The superfluid
component is described by the vortex filament method while the normal fluid is
governed by a modified Navier-Stokes equation. The superfluid vortex lines and
normal fluid components are fully coupled in a self-consistent manner by the
friction force, which induces local disturbances in the normal fluid in the
vicinity of vortex lines. The main focus of this work is the numerical scheme
for distributing the friction force to the mesh points where the normal fluid
is defined and for evaluating the velocity of the normalfluid on the Lagrangian
discretization points along the vortex lines. In particular, we show that if
this numerical scheme is not careful enough, spurious results may occur. The
new scheme which we propose to overcome these difficulties is based on physical
principles. Finally, we apply the new method to the problem of the motion of a
superfluid vortex ring in a stationary normal fluid and in a turbulent normal
fluid.
