A FUZZY LOGIC ALGORITHM FOR ACCELERATION OF CONVERGENCE IN SOLVING TURBULENT FLOW AND HEAT TRANSFER PROBLEMS

Abstract

A novel method for accelerating convergence of iterative computational fluid dynamics (CFD) solvers is reported in this study. The acceleration is achieved by a control algorithm which uses fuzzy logic in order to guide the underrelaxation of the discretized Navier-Stokes equations during code execution. The control criteria are derived from the iterative oscillations of the solution norm observed over a large interval of consecutive iterations prior to the current iteration. The new algorithm was evaluated by solving the problems of mixed convection over a backward-facing step and the natural convection in a rectangular cavity. Both test problems featured highly turbulent fluid flow and heat transfer but entirely different geometric and flow situations. The agreement between the simulation results and the referenced numerical and experimental data was excellent. The computational efficiency of the algorithm was tested by comparing its speed of convergence to the one obtained by using the most optimal constant relaxation factors. In the case of mixed convection over a backward-facing step, the fuzzy control algorithm provided the solution with five times fewer iterations than the solver with the constant relaxation factors. This resulted in a savings of 8 h of CPU time. In the case of natural convection in a rectangular cavity, the fuzzy controller needed only half as many iterations to converge, compared to the solver with the constant relaxation factors. The saving in CPU time was 2 h. The results indicate that the run-time control of underrelaxation has the potential to dramatically improve the computational efficiency of solving a variety of CFD problems with different geometries, boundary conditions, and material properties.