Configuring grub2 on a backup disk

[Jeffrey C. Dege]

I'm running Ubuntu 10.04, and planning to upgrade. Before I do, though,
I want to make sure my backup/restore processes work. My backups, of
course, have been running since I first installed 10.04, but it's only a
restore that can demonstrate that they have been running successfully.

And I've found a problem. I don't know how to get grub2 configured
correctly, on the restored disk.

Currently, my running system is on /dev/sda, with /boot on /dev/sda1
and / on /dev/mapper/desktop-root. (I'm using logical volumes.) This
configuration has been running successfully for several years.

My restore is on /dev/sdb, with /boot on /dev/sdb1 and /
on /dev/mapper/desktop2-root.

All of the files have been restored, and /etc/fstab has been edited, on
the restored drive, to reflect the changed logical volume name.

But I only have grub installed on /dev/sda, so /dev/sdb is not bootable.

I'm not looking to do anything fancy. I'm not trying to dual boot, I
just want to be able to boot from /dev/sdb, using /dev/sdb1 as /boot,
and /dev/mapper/desktop2-root as /. In other words, I want to do
to /dev/sdb exactly what running update-grub would do to /dev/sda, when
I was booted off of /dev/sda.

Any ideas?