Diesel engines will run on Avtur, but the lubricity of Avtur is not as good as Diesel, therefore it will wear out the injector pump quicker.
Adding automotive engine oil can solve this problem but leads to a messy exhaust and rear of your car.
Some Diesel engines have injector pumps that have hardened steel pumping elements to take Avtur, I've only seen these in stationary GSE on the airfield since I've worked in Aviation.
In my past life as a diesel mechanic, I never came across them. I can remember repairing lots of diesel cars from the local RAAF base.......
K