Consistent second-order time-accurate non-iterative PISO-algorithm

Abstract

A new variant of the non-iterative PISO-algorithm for the solution of implicitly discretised fluid flow equations is proposed. The governing equations are discretised in space using a second-order accurate finite volume method. A second-order accurate three-level implicit temporal discretisation scheme is used to discretise the momentum equation, where the non-linear convection term is linearised using a second-order explicit approximation of mass flux at the new time level, based on the results from previous two time steps. In order to ensure temporal consistency on collocated meshes, a consistent Rhie–Chow interpolation for the computation of mass fluxes is used, which is here extended to moving meshes. The proposed non-iterative PISO-algorithm is tested on three fixed and moving mesh test cases, demonstrating its second order accuracy in time.