The numerical technique called upstream differencing, applied to mobility terms in Darcy's law for steam and liquid flow in the geothermal simulators TOUGH and MULKOM, is shown to lead to numerical boundary layers in the equations for steady vertical steam-liquid counterflow. These boundary layers are found to be very narrow, and to act in the same way as capillary
boundary layers, providing reasurance that upstreaming acts to mimic the physical effect of capillarity.

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