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

Abstract

Previous investigations of the time accuracy of the pressure 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 investigation 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 pressure 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 investigators 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.