Oil prices fell on Tuesday on expectations of another rise in U.S. stockpiles and as Saudi Arabia keeps output near record highs, but prices remained near a 2015 peak reached last week. Crude prices have climbed around 16 percent since the start of April due to mounting concern over conflict in Yemen, with the U.S. navy saying on Monday it had sent an aircraft carrier and a guided-missile cruiser into waters near the country. Brent crude for June delivery was down 47 cents at $62.98 a barrel by 0706 GMT (8.06 a.m. BST), after settling flat on Monday. U.S.