Abstract

Previous investigations of the time accuracy of the pressure obtained with fractional step methods have either shown it to be first order in time, irrespective of the order of accuracy of the method, or have presented no pressure results. 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 produces a second order in time pressure. It is shown that the first order behaviour observed by previous investigators was an artifact of the means of testing the accuracy. Finally it is shown that second order pressure can be obtained with the P1 method by using a corrected full pressure.

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