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GRILLIX employs the flux‐coordinate independent approach (FCI), which allows us to study boundary plasma turbulence in realistic diverted configurations. Recently, the physical model in GRILLIX has been extended to a global drift‐reduced Braginskii model, without any separation between background and fluctuations. It includes electromagnetic and thermal dynamics with hot ions, relaxation of the Boussinesq approximation and non‐linear parametric dependencies. This contribution presents solutions to associated issues, that is, the ion diamagnetic polarization and the stiff parallel heat conduction. Simulations based on parameters characteristic for the Alcator C‐Mod tokamak were carried out. In circular geometry, the self‐consistent electric field contains zonal flows and geodesic acoustic modes in the confined region. In the scrape‐off layer, the electron parallel heat conduction and its boundary condition determine the temperature and electric field, leading to sheared flows at the last closed flux surface. [ABSTRACT FROM AUTHOR]