May I ask why you’re querying by username and not by user ID?

You can simply use the author parameter with WP_Query. Using what you linked to as an example:

$args = array(
'posts_per_page' => 10,
'paged' => $paged,
'ignore_sticky_posts' => 1,
'author' => $user_id
);
$query = new WP_Query( $args );

Where $user_id…[Read more]