  This paper addresses how two time integration schemes, the Heun's scheme for
explicit time integration and the second-order Crank-Nicolson scheme for
implicit time integration, can be coupled spatially. This coupling is the
prerequisite to perform a coupled Large Eddy Simulation / Reynolds Averaged
Navier-Stokes computation in an industrial context, using the implicit time
procedure for the boundary layer (RANS) and the explicit time integration
procedure in the LES region. The coupling procedure is designed in order to
switch from explicit to implicit time integrations as fast as possible, while
maintaining stability. After introducing the different schemes, the paper
presents the initial coupling procedure adapted from a published reference and
shows that it can amplify some numerical waves. An alternative procedure,
studied in a coupled time/space framework, is shown to be stable and with
spectral properties in agreement with the requirements of industrial
applications. The coupling technique is validated with standard test cases,
ranging from one-dimensional to three-dimensional flows.
