I just had this issue. So there are a few approaches. The first is that new browsers support the
var formData = new FormData();
Follow this link to a blog with info about how support is limited to modern browsers but otherwise it totally solves this issue.
Otherwise you can post the form to an iframe using the target attribute. When you post the form be sure to set the target to an iframe with its display property set to none. The target is the name of the iframe. (Just so you know.)
I hope this helps