How to force SQL Serve *not* to maintain a log file
There is no way to prevent SQL Server from writing to the transaction log.

In the simple recovery mode, as soon as a transaction finishes its log records are marked so that they can be overwritten but the transaction is still written to the log.

This means that a large transaction can still expand the log, if the current size of the log is too small.

You need to make sure that the drive your log is on has enough adequate free space for the log to expand, or (and this is what I recommend) expand your log file manually to a size that will avoid auto-growth. Do not regularly shrink your transaction log.

The best way to get the correct size for your transaction log is to simulate production traffic on a development server. Run queries (that would be executed against your production database) against your development database for a set period of time, and monitor the log.