Jobs that involve numerical analysis and PDEs?

From what I've read and heard about scientific computing/computational science is that it is perfect for those who have interest in physical problems but like using programming and numerical methods. I've only taken one numerical methods course as an undergrad, but liked it. I also like physics/engineering, so I think this may be a good field for me. I am mostly interested in CFD and numerically solving PDEs However, I heard that most people who get their MS or Phd's related to numerical analysis/PDEs work as software engineers or do work that is mostly programming. There are apparently very few jobs using numerical analysis or numerically solving PDEs, unless it is for work in finance. Is that true?