What happen to schedule flight when airport close for undertermined duration?
If an airport is shut down, all flight operations are ceased, with maybe the exception to police, state or medical flights. Scheduled, non-scheduled and general aviation flights will be grounded until the airport is reopened. 

Flights will be cancelled or the passengers will be bused to airports in the vicinity, from where flights are able to depart, e.g. passengers that were scheduled to depart from Dortmund Airport would be bused to Paderborn Airport. But since the reason for a shutdown usually involves public safety, passengers will be rather evacuated and the flights cancelled, rather then moving them to another airport.