A Unified Fractional-Step, Artificial Compressibility and Pressure-Projection Formulation for Solving the Incompressible Navier-Stokes Equations (Communications in Computational Physics, 2014)
This paper introduces a unified concept and algorithm for the fractional-step (FS), artificial compressibility (AC) and pressure-projection (PP) methods for solving the incompressible Navier-Stokes equations. The proposed FSAC-PP approachfalls into the group of pseudo-time splitting high-resolution methods incorporatingthe characteristics-based (CB) Godunov-type treatment of convective terms with PPmethods. Due to the fact that the CB Godunov-type methods are applicable directlyto the hyperbolic AC formulation and not to the elliptical FS-PP (split) methods, thusthe straightforward coupling of CB Godunov-type schemes with PP methods is notpossible. Therefore, the proposed FSAC-PP approach unifies the fully-explicit AC andsemi-implicit FS-PP methods of Chorin including a PP step in the dual-time steppingprocedure to a) overcome the numerical stiffness of the classical AC approach at (very)low and moderate Reynolds numbers, b) incorporate the accuracy and convergenceproperties of CB Godunov-type schemes with PP methods, and c) further improvethe stability and efficiency of the AC method for steady and unsteady flow problems.The FSAC-PP method has also been coupled with a non-linear, full-multigrid and full-approximation storage (FMG-FAS) technique to further increase the efficiency of thesolution. For validating the proposed FSAC-PP method, computational examples arepresented for benchmark problems. The overall results show that the unified FSAC-PPapproach is an efficient algorithm for solving incompressible flow problems.