That is a really interesting question you are asking ! I may be able to partially answer to it.

Sorry I am on mobile so my answer will not be that long.

As you know, the western Roman Empire fell easy before the Eastern Roman Empire and a lot of knowledge was lost but not all of it : the main centres of knowledge "storing" in the Roman Empire were Constantinople and the Iberian Peninsula. Now, we all know about the Greek Fire that the Byzantine used because they were the only one to have the recipe, but it is interesting to know that the barbaric states that rose from the fall of the western part of the Roman Empire did use the knowledge stored in Iberia. In fact this knowledge was used as soon as the Carolingian Renaissance in the 8th century by the Iberian Christian kingdoms to start the reconquista.

Source : Charlemagne by Georges Minois (it's in French).