Numerical Computation for Modified Cross Model Fluid Flow Around the Circular Cylinder with Symmetric Trapezoidal Cavities

This manuscript explores the flow features of the Modified Cross Model in a channel with symmetric trapezoidal cavities in the presence of a circular obstacle. The non-dimensional governing equations and model for different parameters are evaluated via a Galerkin Finite Element Method The system of non-linear algebraic equations is computed by adopting the Newton method. A space involving the quadratic polynomials ((Formula presented.)) has been selected to compute for the velocity profile while the pressure profile is approximated by a linear ((Formula presented.)) finite element space of functions. Simulations are performed for a wide range of physical parameters such as modified parameter (from 0.0 to 0.5), power-law index (from 0.5 to 1.5), relaxation parameter (from 1 to 3), and Reynolds number (from 10 to 40). For the case of a modified parameter ((Formula presented.)) and relaxation parameter ((Formula presented.)), it is observed that the drag coefficient ((Formula presented.)) shows an increasing trend while the lift coefficient ((Formula presented.)) is changing sign at lower values of ((Formula presented.)), and then becomes positive at (Formula presented.).