That tactic is ... The Platoon Chain.
The chain is what we do, and is in the manuals throughout the end of the war. All those rifle battalions behind the forward battalions are simply on line, at roughly double arm interval, moving forward to occupy ground cleared by the artillery. There is no finesse. They are not highly trained on specific missions like forward battalions.
The main difference between the platoon chain early in the war and late in the war is that early in the war, they attack on wide fronts, with the artillery dispersed over a wide front, and there is not enough mass or coordination to dent the firepower of the average German unit. In the late war period we are concentrating literally hundreds of artillery pieces per kilometer of front, along with close support tanks and assault guns, to literally overwhelm and vaporize the limited number of German me and weapons that can be concentrated opposite to them. We vaporize the immediate front lines, then shove the tank armies through as fast and as deep as we can, until they run out of fuel. All the Germans can do is run fast enough to try and beat the tank spearheads back to the next defensible river obstacle and set up another line of resistance, before enough fuel and ammo gets forward for the Russians to make the next advance.
The thing about Russian battle drills, and they swore by them throughout the cold war, is that is it simply a mathematical problem. You don't have to rely on trying to produce a whole bunch of little tactically brilliant Napoleons and Guderians at the company level and perfect tanks that can knock out 3 or 5 other tanks before they are killed. The limited size army of genius and technological grace is expensive and hard to sustain. The huge army of simple concept that is efficient and sustainable will win. The Russians have always understood this. One guy wandering around through the woods with a $5 million dollar laser blaster is not going to win over 50 guys armed with $10 dollar shotguns.
So anyway, before I digress too far into fantasy land ... some of you are correct. The "wave tactics" were relied on less and less as the war continued. However, it is not correct to assume that something else replaced the wave tactic. It was still THE combat formation and tactic of the rifle units throughout the war. It was relied on less as the war went on, simply due to the fact that firepower was available more and more to destroy resistance ahead of it. Instead of piling up bodies in front of German machineguns, German machineguns were pulverized by artillery fire, then over-run with tanks, with waves of Russian infantry following in amongst the tanks as well as behind them, to mop up whatever was left. The only exception to this is the forward battalions for the initial breakthrough battle.
This tactic was never abandoned by the Red Army, even after it became the Soviet Army. One can watch footage of Soviet offensive tactical training and large scale maneuvers and even read the Soviet manuals, one of which I have for motorized rifle forces dated IIRC, 1986. Infantry are expected to stay in the backs of BMPs and BTRs during the advance, following closely behind the tanks and artillery fire as the artillery fire rolls forward over the objective. Once the BMP/BTRs are 100 meters from the objective, the artillery fire stops and the infantry dismount from the vehicles. They are to immediately form into extended ranks (platoon chain) and move forward on-line, over-run the objective and mop up anything the tanks and artillery have not killed before the defenders can regain their wits and react. They still aren't even trained to kill point targets in this. When they run forward, including RPK squad machinegunners, etc, are all to move forward firing from the hip. The point, just as in WW2, is to keep so much metal going forward as to keep heads down until it is too late to react. It is about firepower and shock effect. A simple math problem.
Now, about the re-enacting URRAH charge. It is a pragmatic approach to an historical simulation. We don't have numbers so we have to simulate them. Russians didn't use 'run-dodge-jump' so we have the advantage of not having to try to train complex styles to people who rarely see each other, being taught by people who know little more than the people they are training. If we can simply keep the people on line and moving forward, that is close enough to reality. We make it a bit more complex by expecting our 'soldiers' to remember to fall down at practical intervals, then get back up again. A bit more complex than the real ones who did this. The leap-frogging death-wave, which fits well into our need to simulate large numbers, adapts itself well to the historical precedent. It is appropriate throughout the war. Another advantage of the Russian system is that it is heavily dependent on artillery and the mortars we've amassed serve this purpose admirably.
The problems with Western Front re-enacting is that it is complex, relies on a lot of initiative from well trained low unit leaders and individual initiative. It also pre-supposes a high level of interaction with a limited number of highly trained and flexible artillery units at the disposal of lower unit commanders. WW2 Western Front re-enactors cannot simulate any of this because it is too complex and that is why Western Front re-enacting is a lame second when it comes to getting the "feel" of what it was like, compared to Eastern Front re-enacting.
So, if we want to do "late war" RKKA re-enacting please do not think that we should be abandoning the URRAH charge and trying to adopt some form of Western tactical concept. The thing we should attempt to simulate, if anything at all beyond the basic URRAH, is the concept of the forward battalion. If so, then what we need to do is get ourself some mortars, some flame throwers, some explosives, breast plates and an SU-76, and practice re-enacting the reduction of strong points in the German main line of resistance. Otherwise, stick to being able to march our soldiers from point A to point B, successfully getting them to get on line at double arm intervals and shoving them forward into the meat grinder. If proof is needed, simply look at the casualty rates all the way through the end of Berlin. It wasn't fancy and graceful, but it worked. That is all that mattered. The genius of the system is at the higher level. All the lower parts are of roughly equal quality and ability. It's where you put them and how you employ them at the higher level that is the critical part.