A SIMPLE-based algorithm with enhanced velocity corrections: The COMPLEX method

• Published in: Computers & fluids Vol. 198; p. 104396
• Main Authors: Aguerre, Horacio J., Venier, César M., Pairetti, César I., Damián, Santiago Márquez, Nigro, Norberto M.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Ltd 15-02-2020; Elsevier BV
• Subjects: Algorithms; Collocated grids; Conservation equations; Finite volume method; Flow stability; Fluid dynamics; Fluid flow; Incompressible flow; Laminar flow; OpenFOAM(R); Segregated methods; Series expansion; SIMPLE algorithm; Stability analysis; Taylor series; Turbulent flow; Velocity; Velocity coupling; OpenFOAM(R); Collocated grids; Finite volume method; SIMPLE algorithm; Segregated methods
• ISSN: 0045-7930; 1879-0747
• DOI: 10.1016/j.compfluid.2019.104396

•A SIMPLE-based algorithm, named COMPLEX, is developed using a Taylor expansion.•A Fourier analysis shows that COMPLEX has better performance than SIMPLE/SIMPLEC.•The stability results are verified solving incompressible flow simulations.•A better convergence rate is found using COMPLEX with high relaxation factors.
This paper introduces a new pressure-velocity coupling algorithm based on the SIMPLEC method. The new approach considers the neighbour velocity corrections of SIMPLEC as a Taylor series expansion, introducing a first-order term to increase the accuracy of the approximation. The new term includes a velocity correction gradient which is assumed to be a scalar matrix constrained by means of a mass conservation equation. The stability of the method is analyzed via a Fourier decomposition of the error showing a better convergence rate than SIMPLE and SIMPLEC for high relaxation factors. The new method is tested in two incompressible laminar flow problems. Then, the analysis is extended to a turbulent flow case. In all cases, the conclusions of the stability analysis are verified. The current proposal sets a theoretical baseline for further improvements of SIMPLE-based algorithms.