A lagged implicit segregated data reconstruction procedure to treat open boundaries

The problem of treating open boundaries is still a challenging one. Applying fully developed condition is constrained to long enough domains. Without having enough physical evidence about what happens on boundaries, the domain extent could not be shortened and computational costs could not be reduced. From the advent of free (open) boundary conditions, they were confined to mixed finite element procedures. Recent works have extended their application to coupled finite volume solvers based on the shape function data reconstruction. A wider class of flow solvers available, however, rely on the segregated procedure where the velocity components and pressure are solved in succession. Moreover, many finite volume algorithms do not use the shape function reconstruction. In this work, by proposing a lagged implicit procedure, we have extended the application of the open boundary condition to these wider classes of flow solvers. The proposed extension is a combination of lagged implicit data reconstruction and overall mass conservation enforcement, which is easily applicable to any segregated and coupled flow solver. To validate the compatibility of this extension, benchmark problem of backward facing step is solved on successively truncated domains, where open boundary may pass through recirculation zones. Results show that the proposed extension works fine. For that problem, it reduced the computational domain length (and hence memory) by a factor of 4.6 and the required computational time by a factor of 21. Flow passing a cylinder is also solved which proves that the method could be applied to external flow problems as well.