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We present a self-consistent 2-D multispecies multi-temperature model of dc nonequilibrium surface plasma discharge phenomena in the presence of a low-pressure imposed high-speed convective flow. For pressures of a few torr and voltages of a few kilovolts, a nonequilibrium glow discharge is generated between the electrodes. Peak charge densities in the discharge on the order of 1014-1016 m-3, electron temperatures on the order of 1 eV, and gas temperatures on the order of 2000 K are observed. Increasing voltages are found to increase the charge density in the discharge and also cause a constriction of the discharge volume. The same trend is also observed with an increase in the discharge pressure. The discharge is highly asymmetric owing to the high-speed convective flow, with the discharge activity restricted to the flow downstream edge of the cathode surface. The convective flow also causes a quasi-neutral plasma-tail-like feature that provides a major loss mechanism for charged and neutral species in the discharge. Despite sufficient cathode surface area, the discharge operates in an abnormal glow mode, with a positive differential resistivity, owing to a flow-induced constricted cathode attachment. Relatively large cathode sheath dimensions on the order of 1 cm are observed with a net electrostatic forcing restricted to this region. The net electrostatic forcing is largely vertical toward the cathode surface, but also has a component in the direction against the flow.