5.21 The PIMPLE algorithm
The - 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 to advection.
For transient simulations, temporal accuracy can be maintained at a higher () 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 with some under-relaxation if necessary.
The simulations can be accelerated to a steady state using local time stepping (LTS). LTS recognises that is limited by the maximum associated with the cell with small and/or high . It uses a field of corresponding to the limit in each cell to accelerate the transient solution. While using a field makes the transient solution invalid, it is acceptable at steady state when .