I have had to deal with this for several years until I had surgery to remove the affected area. They removed about 12 inches of my colon. Prior to the surgery, the doctors recommended a diet in high fiber.
Some foods will cause flare ups and some don't. Each person is different. I would check with your doctor and inquire about a high fiber diet or supplements. According to the Mayo Clinic, "Exactly how diverticula become inflamed or infected isn't clear." And Mayo Clinic also commented, "In the past, doctors thought that nuts, seeds, popcorn and corn played a role in causing diverticulitis by getting trapped in the diverticula. However, recent research has found that these foods weren't associated with an increased risk of diverticulitis."
Check out the Mayo Clinic about this disease.
http://www.mayoclinic.com/health/diverticulitis/DS00070