TY - JOUR
T1 - A Unified Fractional-Step, Artificial Compressibility and Pressure-Projection Formulation for Solving the Incompressible Navier-Stokes Equations
AU - László Könözsy & Dimitris Drikakis
JO - Communications in Computational Physics
VL - 5
SP - 1135
EP - 1180
PY - 2014
DA - 2014/11
SN - 16
DO - http://doi.org/10.4208/cicp.240713.080514a
UR - https://global-sci.org/intro/article_detail/cicp/7076.html
KW - 
AB - <p style="text-align: justify;">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 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 full-approximation 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.</p>