The pressure accuracy of fractional-step methods for the Navier-Stokes equations on staggered grids

Abstract

Previous investigations of the time accuracy of the pres- sure obtained with fractional step methods have shown it to be first order in time, irrespective of the order of accuracy of the method. In this paper a detailed analysis and investiga- tion of the pressure accuracy for P1 and P2 type fractional step methods on staggered finite volume grids is carried out. It is shown that the standard P1 scheme produces a pres- sure that is first order accurate in time, as noted by previous investigators. However the standard P2 scheme is shown to give a second order accurate in time pressure. It is shown that the first order behaviour observed by previous investi- gators for P2 schemes was an artifact of the means of testing the accuracy. Finally it is shown that second order pressure is obtained with the P1 method by using a corrected full pressure.