Avoiding under-relaxations in SIMPLE algorithm

Abstract

The SIMPLE algorithm is devised by interpolating the mass continuity and non-advective momentum equations, provoking apparent simplicity and clarity in the formulation. The SIMPLE variant entitled as the SIMPLE-AC scheme convokes an artificial compressibility (AC) parameter to augment the diagonal dominance of discretized pressure-correction equation. Both methods are characteristically pressure-based, employing a cell-centered finite-volume Δ-formulation on a non-orthogonal collocated grid. A dual-dissipation scheme accompanied by limiting factors, repressing local extrema into the cell-face velocity and pressure, is used to unravel the issue of pressure-velocity decoupling; both SIMPLE and SIMPLE-AC schemes maintain an equivalent scaling (e.g., primary and auxiliary pseudo-time steps remain the same) with the cell-face dissipation and nodal influence coefficients. The phenomenal progress embedded in both contrivances facilitate an avoidance of the pervasive velocity/pressure under-relaxation. However, the SIMPLE-AC algorithm is benefited with using a higher CFL number, enhanced robustness, and convergence compared with the SIMPLE method.