Finite element approximation of biharmonic mathematical model for MHD flow using /spl Psi/-an approach

A generalized mathematical model describing the dynamics of magnetic field influence on a conducting liquid in a square cavity is presented. A method involving a biharmonic mathematical model with stream function /spl Psi/, and the magnetic potential A was used. The Galerkin method was applied to solve a system of two variational identities. A numerical finite element algorithm based on the second order elements was developed. In the algorithm the Newton-Raphson method is used to solve the resulting nonlinear system. Numerical experiments with different Reynolds (R/sub e/, R/sub m/) and Hartmann (H/sub /spl alpha//) numbers were presented in graphical form.