From Longman Dictionary of Contemporary Englishgo swimminglygo swimmingly old-fashionedDO WELLif something you plan goes swimmingly, it happens without problems → swimmingly
Examples from the Corpus
go swimmingly• Everything had been going swimmingly only a moment before.• Things were going swimmingly, what with remarkably honest plumbers, electricians and carpenters fixing up my new home. 