Numerical simulation of steam injection into a water-saturated porous medium may be hindered by unphysical behavior causing the model to slow down. We show how spurious water flow may arise on the boundary between a steam zone and a saturated zone, giving rise to dramatic pressure drops. This is caused by the discretization of the temperature gradient coupled with the direct relation between pressure and temperature in the steam zone. The problem may be a severe limitation to numerical modeling. A solution is presented where the spurious water flow is blocked and this widely enhances the performance of the model. This new method is applied to a previously reported example exhibiting numerical problems. Furthermore, it is applied to the simulation of 2-D sandbox experiments where LNAPL is remediated from a smearing zone by steam injection. These experiments would have been difficult to analyze numerically without the adjustment to prevent spurious flow.