Design of integrated evolutionary finite differences for nonlinear electrohydrodynamics ion drag flow in cylindrical conduit model

Abstract

This research implements an evolutionary optimized finite differences scheme (FDS) for nonlinear electrohydrodynamics ion drag flow dynamics in a cylindrical conduit (EHD-IDFCC). In the scheme, finite differences are exploited to discretize governing expressions of EHD-IDFCC, represented with a nonlinear singular seconder order differential equation, into a nonlinear equations-based system. The fitness function based on residual error is constructed for the FDS-based discretized EHD-IDFCC model. Its optimization is conducted with the global search capability of genetic algorithms (GAs) aided by the local search efficacy of the interior-point method (IPM), i.e., FDS-GA-IPM. The performance of the designed stochastic numerical solver FDS-GA-IPM is evaluated for a variant of the EHD-IDFCC model for different scenarios to measure the effect of axial flow velocity by varying the electric Hartmann numbers, as well as the nonlinearity factor. Statistical interpretations based on histogram illustrations, probability plots, and boxplots in terms of the cost function, mean absolute error (MAE), Thai inequality coefficients (TIC), and coefficient of determination metrics (R2) are used to endorse the accuracy, convergence, stability, and strength of the FDS-GA-IPM.