WordPress: Get current level navigation menu items and their children 1 level deep

page.php

<?php
  //Get the Page Id of the parent
  if ($post->post_parent)
  {
      //There's a parent post lets get the ancestors and grab the top
      $ancestors = get_post_ancestors($post->ID);
      $parentPostId = $ancestors[count($ancestors) - 1];
  }
  else
  {
      //this page is the top most menu item
      $parentPostId = $post->ID;
  }
  $parentNavMenuId=0;
  $menu_name = 'primary';

  if (( $locations = get_nav_menu_locations() ) && isset($locations[$menu_name]))
  {
      $menu = wp_get_nav_menu_object($locations[$menu_name]);
      $menu_items = wp_get_nav_menu_items($menu->term_id);
      $menu_list = '<ul class="left-menu-' . $menu_name . '">';
      
      //Find parent menu id by the post id
      foreach ((array) $menu_items as $key => $menu_item)
      {
          if ($menu_item->object_id == $parentPostId)
          {
              $parentNavMenuIds[] = $menu_item->ID;
          }
      }
      foreach ((array) $menu_items as $key => $menu_item)
      {
          if (in_array($menu_item->menu_item_parent,$parentNavMenuIds))
          {
              $title = $menu_item->title;
              $url = $menu_item->url;
              $menu_list .= '<li><a href="' . $url . '">' . $title . '</a></li>';
              //Echo out children
              $childitems="";
              foreach ((array) $menu_items as $key_possible_child => $menu_item_possible_child)
              {
                //Check if there's any children for this item
                  if($menu_item_possible_child->menu_item_parent==$menu_item->ID)
                  {
                      //Found one lets add it 
                      $title = $menu_item_possible_child->title;
                      $url = $menu_item_possible_child->url;
                      $childitems .= '<li><a href="' . $url . '">' . $title . '</a></li>';
                  }
              }
              if($childitems!="")
              {
                  //if this is not blank we found a child(ren) and should wrap it in a ul
                  $menu_list .= '<ul>'.$childitems. '</ul>';
              }
          }
      }
      $menu_list .= '</ul>';
  }
  else
  {
      $menu_list = '<ul><li>Menu "' . $menu_name . '" not defined.</li></ul>';
  }
  echo $menu_list;
?>