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This paper focuses on the multi-dimensional simulation of non-equilibrium plasma generated by nanosecond pulsed discharge in air, at pressure values higher than atmospheric. Voltage profiles and electrode geometry closely match those from a complementary experimental study. Simulations highlight the transition between different post-discharge plasma regimes at increasing pressure and tie the characteristics of the streamers to the electric field distribution in the gap between the electrodes. Results from simulations match experimental observations and qualitatively capture the experimental trend in terms of regime transition pressure and structure of the streamers. As a result, this paper validates a numerical tool that captures the physical and chemical properties of the low-temperature plasma and contributes to expand the understanding of low-temperature plasma ignition processes.