LIMPO: an improved version of the PISO algorithm for turbulent swirling flows

Introduction The accuracy of computed complex flows is hindered not only by the validity of the particular physical assumptions employed, but also by the accuracy of the numerical schemes used to discretize the set of governing partial differential equations. In order to reduce the inherent discretization errors present in all first-order solution procedures commonly employed these days, a numerical grid comprising a high number of grid points is required, leading to very large central processing unit (CPU) times and highly expensive computations. This situation is particularly severe for complex flows where the detailed geometry has to be described by a large number of grid nodes. One way of reducing the CPU time is to improve the method of solving the pressure-velocity coupled system. The best established methods are the SIMPLE method[1], the SIMPLER[2] and the SIMPLEST[3,4] in which the equations for each variable are solved repeatedly in succession. Others utilize block iteration, such as the SIVA scheme[5], in which the " variables " block is solved simultaneously for a single point (or line). Another iterative method of handling the pressure-velocity coupling arising in the implicitly discretized fluid flow equations – PISO – was presented by Issa[6]. This method was applied by Issa et al.[7] to the computation of two cases of transient axisymmetric laminar flow in circular ducts with abrupt enlargement in both compressible and incompressible situations. The results of the computations were compared with another existing iterative method, and the PISO appeared to be faster than its iterative counterpart for transient flows, either compressible or incompressible, and it exhibited a stable behaviour for large time-step sizes which makes it a reliable technique for steady-state calculations. The choice of the main dependent variables for fluid flows must be such that the primitive variables (i.e., velocity, pressure and density) should be restrained in the equations as the working variables. Either the density is chosen to stand as a main dependent variable, wherein the pressure is evaluated from it via an equation of state, or the opposite is done. The many existing methods developed specifically for incompressible flows, for example Patankar and Spalding[1], choose to treat the pressure, rather than the density, as a main dependent variable. In order to determine the pressure which, while appearing