Frank I would love to collaborate with a storyline, but we dont know the battle that well.
1942 was an interesting year. Stalin, expecting a German summer offensive toward Moscow, concentrated his forces from Voronezh to Leningrad to block it, and sent his southern Army under Timoshenko to launch a spoiling attack againt AG South. However, Hitler planned for a southern offensive, and Timoshenko attacked right into the mass of the German army at Kharkov in May, and got annihilated. AG South had the best units & equipment of the German army at the time. All the panzer divs in AG Center & North were stripped of a Pz battalion which got sent to AG South units to create 3 Pz Battalion Pz Divs, and also give a Pz battalion to each motorized infantry div. In addition, nearly all of the new high velocity Pz III/IV models were in AG South. When Blue got rolling, the Germans owned the battlefield that summer given their new 75L40 weapons in PzIV, Marders & towed weapons. Stalin launched a large tank battle at Voronezh by striking AG Souths left flank & got chopped up.
Hitler burned up his precious fuel that summer by zigzagging his panzers across the Ukraine chasing Red Army phantoms. When the Red Army body count was so low, he convinced himself that the Red Army was finally depleted & split his force in two, one towards Stalingrad, the other towards Baku.
The whole offensive was plagued by supply/fuel shortages & Stalin had just enough time to reinforce Stalingrad, now a pile of rubble as Frank mentioned above, and the Caucasus mountain passes.
Privately, Stalin was pretty spooked when he found out that DDAY/42 wasn't going to happen, and FDR/Churchill thought the USSR would be gone by Xmas. Churchill sent Bomber Command to the Middle East to prepare to torch the Caucasus oil facilities if needed. Turkey started massing troops on the border & it was generally understood that they would declare war if Stalingrad had fell.
As the prolonged urban fight got underway in the city, Stalin noticed Hungarians, Romanians & Italians on the 6th Army flanks, put 2 & 2 together, and did an encirclement on Paulus. The encirclement went well because the fire brigade behind the Romanians (22PD) was short of fuel, & their tanks were in poor mechanical shape the morning of the assault...so they got overrun. Had they been doing proper maintenance, there is a good chance that the encirclement would have failed because the southern arm of the Red Army pincer, while it got through the Romanians OK, ran into serious problems with the 29 mot. ID blocking force. But since the northern arm was bearing down on them, the 29th had to give up the fight & join the Kessel.
There was a critical period of a few days where Paulus could have improved his defensive position by partly withdrawing to Rostov; he would have had the Don river protecting his right flank, and the Volga protecting his left (both still unfrozen), and could have escaped the noose. But Hitler kept him where he was & the rest it pretty well known. The army basically fought on, but gradually faded away from malnourishment & lack of ammo, never formally surrendering. Several thousand Germans lived in the sewers for several months after the last pocket was overrun, and lived underground while their comrades were put to work rebuilding the city.