How to display archive page posts based on author_id

I would like the posts to be displayed on archive page of custom post - gallery based on author_id i.e. the author_id is passed as permalink variable. The posts displayed on archive page would be only those posts published by author whose author_id is passed.

My custom post gallery archive page has the url http://localhost/?post_type=gallery where all the posts posted in the post_type - gallery are listed.

function my_custom_gallery() {
        $gallery_labels = array(
            'name' = _x('Gallery', 'post type general name'),
            'singular_name' = _x('Gallery', 'post type singular name'),
            'add_new' = _x('Add New', 'gallery'),
            'add_new_item' = __("Add New Gallery"),
            'edit_item' = __("Edit Gallery"),
            'new_item' = __("New Gallery"),
            'view_item' = __("View Gallery"),
            'search_items' = __("Search Gallery"),
            'not_found' =  __('No galleries found'),
            'not_found_in_trash' = __('No galleries found in Trash'), 
            'parent_item_colon' = ''               
        );
        $gallery_args = array(
            'labels' = $gallery_labels,
            'public' = true,
            'publicly_queryable' = true,
            'show_ui' = true, 
            'query_var' = true,
            'rewrite' = false,
            'hierarchical' = false,
            'has_archive'        = true,
            'menu_position' = null,
            'capability_type' = 'post',
            'supports' = array('title'),
            'show_ui' = true,
            'query_var' = true,
            'menu_position'      = 4,
            'menu_icon' =  'dashicons-images-alt2'
        );

        register_post_type('gallery', $gallery_args);

    }
    add_action( 'init', 'my_custom_gallery' );

I have introduced a custom query variable using following function

function add_custom_query_var( $vars ){
  $vars[] = "custom_user_id";
  return $vars;
}
add_filter( 'query_vars', 'add_custom_query_var' );

I have rewritten my URL structure to contain the custom_user_id

function add_rewrite_rules($aRules) {
$aNewRules = array('/gallery/user/([^/]+)?$' = 'index.php?post_type=gallerycustom_user_id=$matches[1]');
$aRules = $aNewRules + $aRules;
return $aRules;
}
add_filter('rewrite_rules_array', 'add_rewrite_rules'); 

function rewrite_flush(){
  global $wp_rewrite;
  $gallery_structure = '/gallery/%user_id%/%gallery%';
    $wp_rewrite-add_rewrite_tag("%gallery%", '([^/]+)', "gallery=");
    $wp_rewrite-add_permastruct('gallery', $gallery_structure, false);
  $wp_rewrite-flush_rules();
}
add_action('init','rewrite_flush');


function tdd_permalinks($permalink, $post, $leavename){ 
    $no_data = get_the_author_meta('ID');
    if($post-post_type != 'gallery' || empty($permalink) || in_array($post-post_status, array('draft', 'pending', 'auto-draft'))) return $permalink;
    $var1 = sanitize_title($no_data);
    $permalink = str_replace('%custom_user_id%', $var1, $permalink); 
    return $permalink; 
}
add_filter('post_type_link', 'tdd_permalinks', 10, 3); 

I retrive the custom query variable using $query_author_id = get_query_var(custom_user_id) and want the posts displayed whose author has the author_id - $query_author_id on the archive page.