Control of Convergence in Convective Flow Simulations Using a Fuzzy Rule Set That Stabilizes Iterative Oscillations

摘要

Under-relaxation in an iterative CFD solver is guided by fuzzy logic in order to achieve automatic convergence with minimum CPU time. The fuzzy logic set of rules determines the near-optimal relaxation factor during the execution of the code, based on information from a Fourier transform of a set of characteristic values. The control algorithm was tested on four benchmark problems: buoyancy driven flow in a square cavity, lid driven flow in a square enclosure, mixed convection over a backward facing step and Dean flow. The incompressible Newtonian conservation equations are solved by the SIMPLER algorithm with simple substitution. The relaxation factors for u and v velocities and temperatures are adjusted on each iteration using the fuzzy logic algorithm. Close to optimal convergence is achieved in each of the benchmark cases with nearly minimal number of iterations and CPU time.