You want something like this (untested):
use strict;
use warnings;
my $num_of_sim = shift;
my $me;
chomp($me = `id -un`);
my $PATH = "/home/$me/src/Tc/Scheme4/Simulation$num_of_sim";
open my $fh ,'<', "$PATH/subfile" or die "Cannot open subfile: $!";
my @row_data = <$fh>;
close $fh or die $!;
my $i = 0;
for my $line (@row_data) {
open my $file_out, '>', "$PATH/subfile$i" or die "Cannot open subf
+ile$i: $!";
print $file_out $line;
$i++;
# last if $i > 2967 # Needed if the file has more then 2968 lines
}