White glue(Elmers) is perfectly fine for styrofoam,as long as it doesn't get soaked with water,then it will lose it's grip.The specific glues for styrofoam are waterproof and usually used for architectural decorative applications.A good tip I learned here on the Big A early in my stay was to seal the foam with latex house paint,any color,and then prime and paint as you please or add more terrain and then paint.
cheers!

Contact cement would work well in this situation and it's water proof. You may want to try it if the white glue fails.

Triple,
You can even try Elemer's Wood Glue. It is the yellow glue. It is a bit stronger than the white glue.

I know Woodland Scenics sells a glue for the styrofoam and that is what I used for a few dio's I made with there styrofoam.

The petroleum based solvents will melt and disolve styrene foam as is.The latex paint serves as a barrier so the solvents can't get to the foam.Latex paint is a widely used water soluble/water-soap clean-up paint you find in paint and hardware stores to put on the interior walls of your house.Some brands make exterior grades too.Doesn't matter which you use on the foam though.You probably have a gallon can or 2 in your garage!

Have fun!!