You don't centralize the database, you add the database source to source control just like any other source. Developers work on their individual SQL Server Developer Edition instances, properly licensed for each individual developer on its workstation. If possible, developer may use the Express Edition on their workstation.
Your project does not contain any database binary file (.MDF, .NDF, .LDF), it only contains .SQL source files that, when run, they deploy the current version of the application schema. Developers never operate on the database with DBA tools, they always operate all changes as .SQL scripts added to the source, modifying the deployment procedure accordingly with the schema changes, and providing for appropriate deployment upgrade. See Version Control and your Database.