You can call w3tc_pgcache_flush() from a hook that you put in your functions.php.
/* Flush cache when post is saved */
function clearCache($post_ID) {
if (function_exists(‘w3tc_pgcache_flush’)) {
w3tc_pgcache_flush();
}
return $post_ID;
}
add_action(‘save_post’, ‘clearCache’);