AceShowbiz -

Both Taylor Swift and Calvin Harris have not yet come clean about their romance, but they are said to be sharing some activities they love to do together. One of the activities is cooking, about which a source told PEOPLE, "They cook at home, or order in," adding, "They seem to have a great time together."

The source, moreover, revealed that Swift and Harris did spend time together before the songstress flew to Japan to kick off her six-month long "1989 World Tour" in Tokyo on Tuesday, April 2. "Before Taylor started her tour, she and Calvin spent as much time as possible together," revealed the source. "They seem to be on the same page. They are very low-key and stay at home a lot. They mostly hang out with friends."

Meanwhile, Swift has been reported to have caused at least two arrivals to be delayed at Narita International Airport in Chiba, Japan when she arrived at the venue ahead of her world tour. The 25-year-old singer was mobbed by dozens of enthusiastic fans as she arrived at the airport. And while she was trying to make her way out to the entrance door, some fans reached out to touch her with the others waving their phones and cameras in the air.