9/16 10:17 AM PT -- We're told there was some PDA between Ben Affleck and Jennifer Lopez during the lunch, but it was more to show the kids that they're getting along ... however, this divorce is going to happen according to sources with direct knowledge.

Ben Affleck and Jennifer Lopez are clearly trying to keep their relationship civil as their divorce plays out ... grabbing lunch with their kids -- and, not looking super excited about it.

The estranged megastars went for a bite to eat at the Beverly Hills Hotel Saturday afternoon ... walking in together after the kiddos raced ahead, ready to chow down.

Let's be clear here ... there was absolutely no PDA between Ben and Jenn -- not even the slightest bit of touching. In fact, it seems pretty frigid between the two, if we're being honest.

The pair seemed frustrated to be there at times ... with Ben throwing up his hands and getting close to Lopez's face during their walk-in -- body language that suggests he's not thrilled with his soon-to-be ex-wife.

Ben and Jenn arrived in the same car together BTW ... throwing looks back and forth during the drive up and away from the famous hotel.

It's not surprising this get-together looks so intense ... as we've told you, Jennifer filed for divorce last month sans lawyer -- and, it turns out the two don't have a prenup, so it's a pretty complicated split.

Rumors of the Bennifer split first took off earlier this year when Ben moved out of the couple's massive Los Angeles mansion ... eventually putting the $68 million home on the market.

While false rumors about Ben moving on with Robert F. Kennedy Jr.'s daughter Kick have swirled, J Lo's been spotted out and about ... flexing her abs in crop tops and looking to buy up some impressive L.A. real estate.

Worth noting ... our sources told us the two weren't speaking at all in early August -- so a lunch, even one that looks as intense as this one, is a good sign we gotta say.

That said ... unclear if the two will be getting together for another meal anytime soon.

We've reached out to Ben and Jenn's teams about their afternoon out ... so far, no word back.