The commander I think you are talking about is Ulysses S. Grant
Abraham Lincoln as commander in chief, sent union troops to the South.
Ulysses S. Grant
McDowell
Winfield Scott Henry Halleck Ulysses S. Grant
General Ambrose Burnside
General George G. Meade
General George G. Meade
There were several Union generals in different theaters of war. Scott, Hallack, McClellan, Pope, Burnside, Hooker, Meade, and Grant all served as overall commander of the Union forces as various times.
Alexander
The Union commander was Ulysses S. Grant
The Union commander was Brigadier General Samuel Curtis, the Confederate Comamnder was Major General Earl Van Dorn.
The Union troops were advancing while the Rebel troops were retreating.