Outflowboundary condition for the unsteady-sate fluid flowcomputation with variable density on a collocated grid

This study applies the outflow boundary condition for the unsteady-state variabledensity fluid flow in the staggered grid arrangement to a similar flow in the collocated grid arrangement This application is based on the finite volume method, which successfully satisfies mass conservation. In the staggered grid arrangement, the outflow boundary condition yields the velocities on the outflow boundary using the Neumann condition to relate them to the velocities on the cell face, which are obtained by solving the discretized momentum equations. Here, the Neumann condition instead relates the outflow velocities to those on the cell center. The velocities on the cell face do not always satisfy the discretized continuity equations. Therefore, the velocities on the cell face are corrected using the summation of the discretized continuity equations over the entire computational domain in the staggered arrangement. Moreover, in the staggered grid arrangement, the summation of the discretized continuity equations can be directly obtained since the velocities are defined on the cell face; whereas in the collocated grid arrangement, the summation is evaluated after the Rhie-Chow interpolation since the velocities are on the cell center. As there are different procedures for evaluating the velocities on the outflow boundary in the different grid arrangements, unsteady-state fluid flow computations with variable density in the heating or cooling problems are performed to investigate the applicability of the outflow boundary condition to the collocated grid arrangement. It is found that the outflow boundary condition works well in the collocated grid arrangement and shows excellent mass conservation. Above all, the outflow boundary condition would be applicable to the boundary fitted coordinate system and the unstructured grid, which can treat complex geometries and require the collocated grid arrangement.