What evidence do you have that J. R. R.
Tolkien ever read description of those
battles? What details of those battles can be found in the LOTR? There is one paper in the internet that compares the siege of
Minas Tirith with the Siege of Vienna, but it does not offer much in terms of evidence. In case you means the siege of Vienna where the Polish king Sobiesky was involved, there was a crossing through the wooded
hills to the west of Vienna and a cavalry charge downhill and the siege involved gunpowder and the undermining of
walls. There is no Downhill cavalry charge and no gunpowder and tunneling in the siege of Minas Tirith. There is evidence that Tolkien knew latin and that he studied the Gothic language. As a consequence it is probable that he read Jordanes (who was a Goth and wrote in latin) and that he read the german sagas about Theoderic the Great and the Battle of the Catalaunian
Fields. Miriam Moreno's chapter in a book and her paper include references for her theories.
Tolkien was familiar with a lot of history, but we can't exactly pick his brain for inspirations now.
And yes, there is downhill cavalry charge in Siege of Minas Tirith. Or rather, there is cavalry using wooded hills to sneak around the enemy before attacking. That is something which happened in the Siege of Vienna and the Siege of Minas Tirith, but not on the Catalanuan
plains.
And strategic as well as tactical situation in general is almost identical between the Siege of Minas Tirith and Siege of Vienna, but very different from the Catalaunian Plains. Army of
Gondor is Army of Gondor, not a confederation of barbarian tribes and retinues which Romans employed at the Catalaunian Plains. Vienna is the capital of the Austrian Empire, just as Minas Tirith is the capital of Gondor; there was no capital anywhere near the Catalaunian Plains (capital of the Roman Empire at the time was Ravenna). Majority of the forces at the Battle of Pelennor were provided by Gondor, just as majority of the relief force at the Siege of Vienna were actually Habsburg troops - but in both cases, far more focus is given to the allied cavalry charge (
Rohirrim / Polish). Meanwhile, majority of Aetius' troops were actually allied barbarians (Alans, Germans, Visigoths). Number of Rohirrim cavalry at the Battle of Pelennor is 6 000 - which just so happens to be exactly twice the number of the Winged Hussars (3 000) but one-third the number of overall cavalry (18 000) which participated in the Relief of Vienna. Meanwhile majority of the forces at Catalaunian Plains were infantry - and it were the Huns which had cavalry advantage, whereas at both Vienna and Pelennor the cavalry advantage was with the allied force. At Catalaunian Plains, battle was dominated by a sharp ridge which played a major part as a contested terrain point - at both Vienna and Pelennor, wooded hills provided cover for the approaching allied cavalry, but had no impact on the battle itself.
Of course, this is not to say that Catalaunian Plains have no influence on / similarities with the Pelennor:
Theoden's role, fate and even name are strongly reminiscent of king Theodoric. Theodoric was believed to have been thrown from the
horse and trampled, whereas Theoden died under Snowfire. But this merely means that Tolkien had more than one inspiration, not that everything in previous paragraphs is irrelevant / can just be dismissed. And Tolkien
was familiar with the history of Central and Southeastern Europe; as I recall, he visited Italy at the very least. You might want to read through discussions on topic I had elsewhere on the site: