The role of mass conservation in pressure-based algorithms

Two numerical issues important to proper problem specification for pressure-based algorithms are investigated, including (1) well posedness of the pressure-correction equation, and (2) proper prescription of flow variables at open boundaries, particularly if inflow occurs. Lid-driven cavity flow and flow past a backward-facing step are used to help discuss the issues. It is shown that during each iteration, the explicit enforcement of global mass conservation is important even for the intermediate, nonconvergent flow field in order to maintain good convergence rates. This requirement stems from the fact that the pressure distribution is an outcome of the continuity equation. Furthermore, it seems that the global continuity constraint is often sufficient for the numerical problem for a flow with an open boundary to be well posed, regardless of whether or not inflow occurs at that boundary. Thus, in the pressure-based algorithm with a staggered grid the downstream boundary can, if necessary, pass through a recirculation region without adverse effects on solution accuracy.