Modified fractional-step methods for the Navier-Stokes equations

Abstract

Fractional step methods integrate the Navier-Stokes equations in a non-iterative fashion. The commonly used P2 pressure correction fractional step method introduces a second order in time error into the solution as a result of the non-iterative approach. In this paper two alternative fractional step methods are examined in which the additional error is third order in time. One of the methods extends the standard P2 method to increase the accuracy of the approximate pressure included in the momentum equations, and is denoted the P3 method. The other method solves a Poisson pressure equation prior to the solution of the momentum, and is denoted the pressure method. Both alternative methods are shown to reduce the overall error and increase the efficiency as compared to the standard method.