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

Abstract

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.