A Unified Fractional-Step,Artificial Compressibility and Pressure-Projection Formulation for Solving the Incompressible Navier-Stokes Equations

This paper introduces a unified concept and algorithm for the fractionalstep(FS),artificial compressibility(AC)and pressure-projection(PP)methods for solving the incompressible Navier-Stokes equations.The proposed FSAC-PP approach falls into the group of pseudo-time splitting high-resolution methods incorporating the characteristics-based(CB)Godunov-type treatment of convective terms with PP methods.Due to the fact that the CB Godunov-type methods are applicable directly to the hyperbolic AC formulation and not to the elliptical FS-PP(split)methods,thus the straightforward coupling of CB Godunov-type schemes with PP methods is not possible.Therefore,the proposed FSAC-PP approach unifies the fully-explicit AC and semi-implicit FS-PP methods of Chorin including a PP step in the dual-time stepping procedure to a)overcome the numerical stiffness of the classical AC approach at(very)low and moderate Reynolds numbers,b)incorporate the accuracy and convergence properties of CB Godunov-type schemes with PP methods,and c)further improve the 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 fullapproximation storage(FMG-FAS)technique to further increase the efficiency of the solution.For validating the proposed FSAC-PP method,computational examples are presented for benchmark problems.The overall results show that the unified FSAC-PP approach is an efficient algorithm for solving incompressible flow problems.