5.21 The PIMPLE algorithm

The eqn-eqn coupling algorithms in Sec. 5.12 and Sec. 5.19 can be combined into an algorithm known as PIMPLE. PIMPLE merges the controls of PISO and SIMPLE (hence the merged acronym), in particular the iterative loops and under-relaxation.

All controls are optional; the standard transient algorithm is replicated by deactivating both the under-relaxation and the PIMPLE loop. By including the PIMPLE loop, equations are solved using variables updated within the time step. Accuracy is improved in particular due to the update of matrix coefficients from the contribution of eqn to advection.

For transient simulations, temporal accuracy can be maintained at a higher eqn (eqn) using a second order time scheme (Sec. 3.18 ) combined with iterations of the PIMPLE loop. Similarly, the PIMPLE loop can update explicit source terms, e.g. in energy or momentum, to improve accuracy.

Pseudo-transient solution

PIMPLE can be configured to produce a steady flow solution quickly by a pseudo-transient simulation. These simulations are not intended to capture realistic transient behaviour so can run at eqn with some under-relaxation if necessary.

The simulations can be accelerated to a steady state using local time stepping (LTS). LTS recognises that eqn is limited by the maximum eqn associated with the cell with small eqn and/or high eqn. It uses a field of eqn corresponding to the eqn limit in each cell to accelerate the transient solution. While using a eqn field makes the transient solution invalid, it is acceptable at steady state when eqn.

PICT\relax \special {t4ht=

Notes on CFD: General Principles - 5.21 The PIMPLE algorithm