wordpress get children of category

gistfile1.txt

/**
    $term_id = 1;
    $taxonomy_name = 'category';
    $args = array( 'parent' => $term_id);
    $termchildren = get_product_children($term_id, $taxonomy_name);
**/
function get_product_children( $term_id, $taxonomy ) {
    if ( ! taxonomy_exists( $taxonomy ) ) {
        return new WP_Error( 'invalid_taxonomy', __( 'Invalid taxonomy.' ) );
    }
    $term_id = intval( $term_id );
    $terms = _get_term_hierarchy($taxonomy);
    if ( ! isset($terms[$term_id]) )
        return array();
    $children = $terms[$term_id];
    foreach ($children as $key=>$child ) {
            unset($children[$key]);
            $children[$child] = get_term_children($child, $taxonomy);
    }
    return $children;
}