Mormon does not give us the details of this battle, even though it was the largest battle in Nephite history, to that point. His motivation for describing the many wars in the end of Alma is not just for the sake of military history but rather to teach us many important lessons. The details of this tremendous battle apparently would not be helpful for us.
What is interesting is to recognize the scale and scope of Nephite/Lamanite battles. Their battles equal the great battles of the last two centuries in terms of casualties. The commentary for Alma 2:19 describes a previous battle in which the casualties were on the same scale as the bloodiest battles of the Civil War and World War II. This conflict, according to Mormon, was an even greater slaughter, yea, and tens of thousands of the Lamanites were slain and scattered abroad. Yet, the exact number was not counted, Now their dead were not numbered because of the greatness of their numbers; neither were the dead of the Nephites numbered (Alma 30:2).