The numerical simulations are consisted of two parts : the first is to simulate the friction reduction by microbubbles on a flat plate ; the second is to simulate initially the friction reduction on the approximated ship model with the flat bottom 本文对微气泡减小表面摩擦阻力的现象进行了数值计算。数值模拟分成两个部分：第一部分是平板微气泡减阻的数值模拟；第二部分是平底近似船模数值模拟的初探。
