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Advanced divertors gain larger plasma wetted area by poloidal or total flux expansion. Qualitative characteristics of supersonic plasma flows which are generated by the magnetic nozzle effect are studied by using a plasma fluid model incorporating anisotropic ion pressure (AIP model). The AIP model can self-consistently simulate supersonic plasma flows because, unlike the widely-used plasma fluid model (the Braginskii equations), the equation of parallel plasma momentum in it is described as a hyperbolic-type and the plasma flow velocity is solved without using explicit boundary conditions at the sheath entrance in front of divertor plates. In comparisons of plasma profiles between the AIP model and the Braginskii equations, it is observed that the plasma flow velocity in the Braginskii equations is forced to the sound speed at the sheath entrance in conditions of decelerating supersonic plasma flows leading to qualitative deviations with the AIP model. In an application of the AIP model to a scrape-off layer/divertor region incorporating super-X divertors with various flux-expansion ratios, supersonic plasma flows in divertor regions and highly anisotropic ion temperatures are successfully simulated. It is also demonstrated that it becomes easier with the AIP model to explain the mechanisms of generations of supersonic plasma flows and acceleration/deceleration of them (including stationary shock waves) in flux-expanding divertors from the mirror effect point of view. [ABSTRACT FROM AUTHOR]