Can pbkdf2 be used with a fixed salt to give a deterministic slow hash?

I need a password hashing function that is deterministic. Correlation attacks are not a concern. The same password must produce the same hash. I just want to protect the password against dictionary and brute force attacks in the event that the hash is leaked.

Is there a well known way to do this? Would fixing the salt of bcrypt/PBKDF2/scrypt be enough?

• Note that the good practice would be either to derive the salt in a deterministic way (from the username, for example) That is a brilliant idea. Thanks! – Daffy Jul 16 '17 at 16:15