Summary: A numerical simulation of the time evolving layered structure in a fluid supporting both temperature and salinity gradients was conducted in an L- shaped region where an initially stable salt-stratified fluid was disturbed by heating the wall containing the corner protruding into the flow. In order to resolve the interfacial gradient between each layer of the flow a recently developed pseudospectral-element matrix method using the primitive variable formulation of the Navier-Stokes equations was incorporated into a new implementation of the Schwarz alternating procedure for Navier-Stokes solutions which differs from the conventional technique. This new procedure directly employs the continuity equation at the edge of overlapped domains as the boundary condition for the pressure rather than a Dirichlet condition. A novel feature of this method is that it allows the use of a previously developed eigenfunction expansion of the pressure operator to reduce the original complex two-dimensional problem to a simple one-dimensional problem. The computational results show that not only are convective layers formed along the vertical wall above the corner but, surprisingly, the layer emanating from the corner region dominates the development of the upper and lower layers.