Check out polished bliss website, car care advice.
I have black paint with swirls like you, Audi paint is notoriously hard and hand polishing is virtually impossible.
Quote from their website;
Being brutally honest, you have almost no chance of correcting swirl marks and light to moderate defects (fine scratches and etching) on your car by hand. The best you could hope to achieve making multiple attempts per panel with a light compound like Menzerna Power Finish (203S) in conjunction with Lake Country Light Cut Hand Pads is around 50% correction, and even this would require a huge amount of time and effort to achieve. Therefore, our advice is to consider alternative options such as glazing, machine polishing or using the services of a professional detailer. Layering filler heavy glazes such as R222 Gloss Enhancing Paintwork Cleanser or Poorboy's Black Hole Glaze with Meguiar's Microfibre Applicator Pads can give the illusion of a reasonable level of paint correction for relatively little effort, and this effect will usually last for between three to six months at a time if a good quality last step product is used regularly to protect the resulting finish. Investing in a machine polisher makes more sense if a high standard of permanent correction is desired, but considerably more time and money will have to be invested in both products and the learning of new techniques. For those enthusiasts desiring a high level of correction but not wishing to entertain the idea of machine polishing their own paint, using the services of a professional detailer to get the paint back up to standard can be an equally cost effective way forward.
I use Poor Boys Black Hole. It really does work.
