Negative Supply Voltage
Theoretically that will work, but only if V2 is a floating (isolated) supply. Many power supplies are actually referenced to the protective earth AKA 3rd prong. These would not obviously work. 

For an easy way to generate -12V from +12V, you can use a buck-boost SMPS circuit. TI SLYT286 shows how to use a common buck-converter in an inverting buck-boost configuration. Do note that this will effectively double the voltage so you need something that's OK with 24VDC input. You can obviously use a dedicated buck-boost converter but for actual product designs it's beneficial to use same parts if you can. 

http://www.ti.com/analog/docs/litabsmultiplefilelist.tsp?literatureNumber=slyt286&amp;docCategoryId=1&amp;familyId=751&amp;keyMatch=SLYT286&amp;tisearch=Search-EN-Everything

If you really want to get fancy, you can do +/- output SMPS circuit using a common mode choke but that's a bit beyond the scope here.