An analysis and comparison of the time accuracy of fractional-step methods for the Navier-Stokes equations on staggered grids

摘要

Fractional-step methods solve the unsteady Navier-Stokes equations in a segregated manner, and can be implemented with only a single solution of the momentum/pressure equations being obtained at each time step, or with the momentum/pressure system being iterated until a convergence criterion is attained. The time accuracy of such methods can be determined by the accuracy of the momentum/pressure coupling, irrespective of the accuracy to which the momentum equations are solved. It is shown that the time accuracy of the basic projection method is first-order as a result of the momentum/pressure coupling, but that by modifying the coupling directly, or by modifying the intermediate velocity boundary conditions, it is possible to recover second-order behaviour. It is also shown that pressure correction methods, implemented in non-iterative or iterative form and without special boundary conditions, are second-order in time, and that a form of the non-iterative pressure correction method is the most efficient for the problems considered.