The equilibrium position of a deformable bubble in a Combined Couette-Poiseuille flow was investigated numerically by solving the full Navier-Stokes equations using a finite difference/front tracking method. The effectiveness of the present approach to predict the migration of a bubble in a Combined Couette-Poiseuille flow was examined, and the behavior of the bubble migration with different Reynolds numbers was investigated. The related unsteady incompressible full Navier-Stokes equations were solved using a conventional finite difference method with a structured staggered grid. The interface was tracked explicitly by connected marker points via front tracking method. One field approximation was used, while one set of governing equations was only solved in the entire domain and different phases treated as one fluid with variable physical properties. The interfacial effects are accounted for by adding appropriate source terms to the governing equations. Since the interface deforms continuously, it is necessary to restructure its grid as the calculations proceed. The purpose of this study was to examine the lateral position of the bubble by using finite difference/ front tracking, ANN and ANFIS methods. Also, estimated values of the lateral position of the bubble by ANN and ANFIS methods were compared with front tracking method, to select the best method.
