Exploring SIMPLE algorithm for all speeds

Abstract

The segregated SIMPLE algorithm is developed on a curvilinear collocated grid using a cell-centered finite-volume Δ-formulation to speculate all-speed fluid flows. The occurrence of velocity-pressure decoupling is unraveled by invoking a consistently formulated dual-dissipation scheme. A modified flux-difference scheme calculates viscous fluxes at all speeds. A local Mach number based indicator is initiated to impose a constraint on the actual state of compressibility, related to the density-updating in the corrector step of SIMPLE algorithm. The positivity in influence coefficients’ diagonal-dominance with the corrector step is guaranteed by the current contrivance, preventing the need for an under-relaxation (UR) factor. For a selected low Mach number flow, comparisons reveal the relevance of incompressible approach, sprung from the unique compressible solver.

Keywords

• SIMPLE algorithm
• Under-relaxation
• Compressibility
• Diagonal dominance
• Convergence and robustness