Solutions to the flow equilibrium problem in elliptic regions

The existence of poloidal flow transforms the elliptic Grad-Shafranov-Schluter (GSS) equation into an EGSS system (Extended GSS) of partial differential equation and an algebraic Bernoulli's equation. The EGSS system becomes alternatively elliptic ad hyperbolic as the Mach number of the poloidal flow increases with respect to the Alfven speed of the poloidal magnetic held. A computer program for solving EGSS equations in elliptic regions using the inverse method and Fourier decomposition has been prepared. The solutions in the first and second elliptic regions have been found for different plasma cross-sections, not necessarily up-down-symmetric. The solutions in different elliptic regions exhibit the significant differences in the poloidal magnetic field configuration and the shifts between magnetic axis and density axis differ in sign and magnitude.