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Non-equilibrium plasma generated from positive-pulsed nanosecond electrical discharges into desiccated air is simulated in this paper using a multi-dimensional, multi-physics plasma solver. A pin-to-pin electrode configuration is used with a fixed 5.2 mm gap spacing. Peak pulse voltages range between 10.2 and 22.5 kV. Care is taken to match the exact electrode profile from the experiments, and adjust the electron collision frequency so that breakdown limits closely match those from corresponding experimental results. The optimized numerical simulations predict qualitative streamer structure that is in close agreement with experimental observations. Quantitative measurements of atomic oxygen at the anode tip and qualitative estimates of streamer gas heating are closely matched by simulations. The model results are used to provide insight into the spatial and temporal development of the transient plasma. The work performed in this paper delivers a numerical tool that can be extremely useful to link the post-discharge plasma properties to low-temperature plasma ignition mechanisms that are of great interest for the automotive industry.