I work on a project that requires many on-site meetings at the client's location, with client people from different departments. These departments can be considered as closed silos, where everyone knows only the things they care about, and nothing more (obviously some people are more open whereas others follow this policy strictly). For example, we recently attended a two-hour meeting with 18 people from 9-10 different departments to discuss the position, the color and the label of a single button in a web page.
Because of politics/personal dislikes/etc(I don't exactly know), some meetings become very heated: I could cite countless times where people yell at each other, I could cite a dozen times when people insult each other (many-a-time personal insults) and I personally saw yesterday people start a physical fight1 (the reason I decided to ask this question).
How should I behave the next time I will be in such a situation? Should I directly intervene to separate the contenders? Should I try to stop the heated meeting from becoming a fight? Should I stay in my corner and not get involved?
1 A coworker and I were in a meeting with 7 people from 4 departments of the client. Two of these departments are in a big delay: this delay will probably cost the company a huge fine (a million). Immediately people start to shout at each other and in less than 5 minutes, they were launching insults at each other. In the meanwhile, my coworker and I were in a corner speechless. After a few minutes, 3 other people join the meeting and the situation escalated: someone blinded by anger threw his laptop at other people and broke the glass door of the meeting room. At this point, 4 or 5 people began a physical fight. A lot of people came in and, with a lot of difficulty, they separated the contenders. We were asked to return to our office.