Re: BDR - Failure of Primary Server - How to recover?

You switch to writing to the secondary, presuming that you're not already doing so (it's multi-master), stop writing to the old primary, and remove the old primary using bdr.bdr_part_by_node_names(...).

Data that was committed to the old primary but not yet replicated is lost; if you can't deal with that you'll need synchronous replication.

I would be more inclined to use normal streaming replication and hot standby for a simple master/replica failover scenario, though UDR (or BDR in subscribe mode) is becoming quite useful for this use case too. If you don't need multi-master, don't use multi-master.