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.

TMZ.com

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.