I find no ruling in the Core Rulebook FAQ, so the general Combining Magic Effects rules apply:
Stacking Effects: Spells that provide bonuses or penalties on attack rolls, damage rolls, saving throws, and other attributes usually do not stack with themselves.
Same Effect More than Once in Different Strengths: In cases when two or more identical spells are operating in the same area or on the same target, but at different strengths, only the one with the highest strength applies.
Same Effect with Differing Results: The same spell can sometimes produce varying effects if applied to the same recipient more than once. Usually the last spell in the series trumps the others. None of the previous spells are actually removed or dispelled, but their effects become irrelevant while the final spell in the series lasts.
Neither spell provides a bonus or penalty, but the sections following the 'Stacking' segment are not only regarding bonuses, as evidenced by the section on Multiple Mental Control Effects.
So, the continuing damage would overlap, not stack, as each effect is indeed identical. The only benefit to multiple castings would be to continue the duration.
Clarification: Damage dealt always stacks, but multiple identical effects dealing damage do not stack.
A creature hit by 3 acid arrows takes 6d4 acid damage this round, and only 2d4 acid damage the next. This is because the acid damage is caused by a continuing effect, not an instantaneous residue.
Had the spell description shown "Duration: Instantaneous", and the rules text said "the acid conjured lasts for 1 round per caster level, unless neutralized, dealing 2d4 damage each round it lasts", then the cause of the damage would have stacked.