Control of convergence in a computational fluid dynamics algorithm using fuzzy logic

Under-relaxation in an iterative CFD solver is guided by fuzzy logic to achieve automatic convergence with minimum CPU time. Two fuzzy sets of rules were developed in order to determine the near-optimal relaxation factor during the execution of the code. The first set of rules was based on comparing the iterative errors and their changes with the maximum value of the solution in the computational domain. The second set of rules used the information from a Fourier transform of a set of characteristic values. The rule sets adjust the relaxation factors for the system variables on each iteration and restart the solver if divergence occurs.; The control algorithms were evaluated on the total of eight benchmark problems. The laminar flow problems include buoyancy driven flow in a square cavity, lid driven flow in a square enclosure, mixed convection over a backward facing step and Dean flow. Two turbulent problems based on K-ϵ model are solved. They include buoyancy driven flow in a rectangular cavity and mixed convection over a backward facing step. A radiation heat transfer in a 1-D fin was treated, as well. The incompressible Newtonian conservation equations are solved by the SIMPLER algorithm with simple substitution. Radiation heat transfer in a fin was solved by another finite difference solver in order to show generality of application of the fuzzy control algorithms. Close to optimal convergence was achieved in each of the cases, with nearly minimal number of iterations and CPU time. In order to achieve the best performance of the fuzzy controller, the membership functions were tuned by using gradient method.; Fuzzy control of the relaxation factors provided a solution to highly difficult numerical models, where any selection of constant relaxation factor resulted in divergence. The choice of the relaxation factors for a given problem became independent from the user's skill or experience with the particular problem.