Computationally intelligent CFD: Solving potential, viscous and non-Newtonian fluid flow problems using real-coded genetic algorithms

Fluid flow simulations are often hindered by divergence or slow convergence. The concept of evolutionary search is utilized to solve a number of fluid flow problems via a real-coded genetic algorithm (GA). Genetic algorithms mimic the natural evolution process found in nature. They are governed by the Darwinian principle of natural selection, best described by the phrase "survival of the fittest." Specifically, a real-coded genetic algorithm (GA) heuristically searches the solution domain not particularly affected by gradients in the flow field which are one of the main causes of divergence. The heuristic nature of GA's allows them to avoid solving systems of equations in order to get a solution. This precludes many convergence difficulties associated with the stiffness of models. Further, these stochastic optimization techniques work around many stability issues in computational fluid dynamics, such as those arising from large time steps when seeking steady solutions.; Finite difference and finite volume discretizations are used as GA objective functions. A new refinement strategy is proposed whereby the algorithm starts with a coarse solution and works its way toward increasing detail by adding more nodal points. To further reduce the number of optimized variables in the GA, a GA window is proposed that breaks up the domain into many subproblems and spans the flow domain in an incremental fashion. A number of new mutation schemes and other genetic operators are also proposed which enhance the search even further.; The GA is used to solve problems in potential flow, viscous flow via the Navier-Stokes equations, and non-Newtonian flow with the power law model, where the problem of flow over a backward facing step was studied. The SIMPLER finite volume algorithm was used for validation and comparison. On many occasions, the GA was able to solve problems that the gradient-based method could not. This is mainly due to the relative indifference of the GA to places of high gradients when performing the search. The idea is to use GA's as auxiliary solvers to be activated when common methods encounter difficulties converging. This work shows genetic algorithms to be of great potential in CFD analyses.