Application of non-pressure-based coupled procedures for the solution of heat and mass transfer for the incompressible fluid flow phenomenon

Abstract

MotivationThe inconvenient treatment of the current velocity-pressure coupling strategies is still a debating issue. Whether the procedures are formed on coupled or segregated solution strategy, the substituted equation for pressure, which is applied instead of the original continuity equation, is known to cause convergence problems for complex fluid flow situations. Challenge and approachThe present study aims to evaluate two fully implicit, non-pressure-based coupled algorithms known as FICS and SICS (Fully/Simplest Implicit Coupled Procedures) that are able to solve the flow equations without utilizing any additional formulations (Poisson-type or else) for pressure. To do so, a numerical code using C++ was developed, and the noted coupled procedures were implemented alongside the well-known SIMPLEC (Semi-Implicit-Pressure-Linked-Equation-Consistent) algorithm, which was utilized as a benchmark procedure. The evaluations of the noted algorithms seek to compare the stability, solution speed, and compatibility to various physical phenomena such as turbulence and heat transfer that are the main subjects used to compare the fluid mechanic procedures. Significant resultsObtained results indicate that coupled procedures are irrefutably stable whether only the laminar equations are solved or other highly influential scalar equations have participated. As an instance, it was observed that FICS-2 achieved convergence at least two times faster than SIMPLEC while applying the least amount of relaxation to amend for both non-linearity and the pressure-velocity coupling. Impact of the study and conclusionAs a result, it is concluded that the primitive form of continuity equation is a more efficient alternative than the standard Poisson-based formulation and could be considered for future developments in commercial CFD purposes.