The northern continental slope of the Gulf of Mexico is riddled with numerous subsiding diapiric minibasins bounded by ridges, and often connected by channels created by turbidity currents. The region is economically relevant in that these diapiric minibasins constitute excellent focal points for the deposition of sand. These deposits in turn serve as excellent reservoirs for hydrocarbons. A better understanding of the "fill and spill" process by which minibasins fill with sediment as the intervening ridges are dissected by canyons may serve to aid in the location of such reservoirs. A theoretical analysis in a companion paper has revealed two key aspects of the "fill and spill" process: (1) the formation of an internal hydraulic jump as a turbidity current spills into a confined basin, and (2) the detrainment of water across a settling interface forming at the top of the ponded turbidity current downstream of the hydraulic jump. In that paper it was shown that sufficiently strong detrainment can consume the flow, so that there is no outflow of either water or sediment even with continuous inflow. As the basin fills with sediment, however, overspill is eventually realized. Herein the theory of the companion paper is used as the basis for a numerical model of ponding of turbidity currents. The numerical model is tested and verified against two experiments. In the first of these, detrainment is sufficient to capture an entire sustained turbidity current. In the second of these, detrainment is insufficient to prevent sustained overspill. The principles of similitude using the densimetric Froude number allow upscaling of the experimental results to field scale. A full numerical model is verified against the experiments and applied at field scale. The result is a view of intraslope minibasin sedimentation that has a stronger physical basis than the conceptual models proposed to date.