After a quick search of three sites, there isn't one. There is a term for anti-siege warfare, poliorcetics, but not a description. U.S. military doctrine does not have besieging as a tactic. So, no counter-siege doctrine? That seems hard to believe.
On Wikipedia's "Siege" page there is the counter-siege tactic of the "airbridge". Like Berlin Airlift--which was resupplying a civilian population, which is what we have in Ukraine's cities. Obviously, you have to have freedom of movement in the skies for the airbridge to work. The Russians in Ukraine though do not have air superiority and Ukraine use of drones
Throughout the war both the Western Allies and the Germans tried to supply forces besieged...
Different! Not civies, armies.
...behind enemy lines with ad-hoc airbridges. Sometimes these attempts failed, as happened to the besieged German Sixth Army the siege of Stalingrad,
Now Stalingrad is a variation: There the invading army got trapped. Having just read The Rise and Fall I know that Hitler repeatedly called for his commander, Paulus, to counter-attack. We have civilians in Mariupol. Civilians and military in Kyiv, however.
...and sometimes they succeeded as happened during the Battle of the Admin Box (5 – 23 February 1944)...
Admin Box was a besieged army successfully holding out--because of air resupply.
and, during the short Siege of Bastogne (December 1944). Bastogne was a town, not a city, and the siege was of an army not a civilian pop.:
...American soldiers were outnumbered approximately 5 to 1 and were lacking in cold-weather gear, ammunition, food, medical supplies, and senior leadership...Due to the worst winter weather in memory, the surrounded U.S. forces could not be resupplied by air nor was tactical air support available due to cloudy weather.
[The Germans] us[ed] their mobility to isolate Bastogne...rather than attacking Bastogne with a single large force. This played into the American advantage of interior lines; the defenders were able to shift artillery fire and move their limited ad hoc armored forces to meet each successive assault.
That is what the Russians are doing to a civilian population in Mariupol and to a civ-military pop in Kyiv. Mariupol is starving to death so apparently the "airbridge" is not possible. I think Mariupol is fucked.
Several times during the Cold War the western powers had to use their airbridge expertise.
- The Berlin Blockade from June 1948 to September 1949, the Western Powers flew over 200,000 flights, providing to West Berlin up to 8,893 tons of necessities each day.
- Airbridge was used extensively during the siege of Dien Bien Phu during the First Indochina War, but failed to prevent its fall to the Viα»t Minh in 1954.
- In the next Vietnam War, airbridge proved crucial during the siege of the American base at Khe Sanh in 1968. The resupply it provided kept the North Vietnamese Army from capturing the base.
USMA.EDU:
Recent historical examples of city attacks in limited warfare where an attacking force attempted to kill the defenders or seize the city include:
Hue, Vietnam: January 31 1968 to March 3, 1968
Vukovar, Croatia: August 25, 1991 to November 18, 1991
Sarajevo, Bosnia and Herzegovina: April 5, 1992 to 29 February 29, 1996
Grozny, Chechnya: December 31, 1994 to February 8, 1995
Grozny, Chechnya: December 25, 1999 to February 6, 2000
Fallujah, Iraq: April 4, 2004 to May 1, 2004
Fallujah, Iraq: November 7, 2004 to December 23, 2004
Military operations against enemy-held cities have become increasingly frequent. In the last eight years, there have been twelve distinct major urban battles involving city attacks. These have occurred in the ongoing civil war in Syria; against the Islamic State in Iraq, Syria, and the Philippines; and between government and Russian-backed separatist forces in eastern Ukraine. Among the most recent examples are:
Aleppo, Syria: July 19, 2012 to December 22, 2016
Ghouta, Syria: April 7, 2013 to April 14, 2018
Deir ez-Zor, Syria: July 14, 2014 to September 10, 2017
Ilovaisk, Ukraine: August 7, 2014 to September 2, 2014
Kobani, Syria: September 13, 2014 to January 26, 2015
Debal’tseve, Ukraine: January 14, 2015 to February 20, 2015
Ramadi, Iraq: August 11, 2015 to February 9, 2016
Fallujah, Iraq: May 22, 2016 to June 29, 2016
Mosul, Iraq: October 16, 2016 to July 20, 2017
Raqqa, Syria: November 6, 2016 to October 17, 2017
Marawi, Philippines: May 23, 2017 – October 23, 2017
Tal Afar, Iraq: August 20, 2017 to September 2, 2017
In short, there is no go-to tactic to defeat a siege. USMA says the defenders, civies and military, have a clear, significant advantage in cities. However, in Ghouta Russian-Syrian air forces used chemical weapons to conquer the civilian-rebel resisters. That is what they are going to do in Kyiv. It's up to Volo: his options, it seems to me are to counter-attack in Mariupol and Kyiv to break the sieges or to surrender.
