Several different grasses are commonly called dune grass. All of them are very invasive and extremely hard to kill. If not killed dune grasses will spread, mainly by rhizomes (roots which grow new grass) until it has taken over almost every square inch of your yard.
Dune grass is tolerant of poor soil and even salt. Killing dune grass which has already grown among your other grass or plants may require the elimination of those grasses and plants as well.
Spread a black tarp over your dune grass and weigh down the edges of the tarp so it stays in place. Leave the tarp over the grass for 14 days. Dune grass is a sun-loving grass and depriving it of light kills its leaves and weakens its root system.
Remove the tarp and rototill the soil, exposing as many of the roots as possible. Use a hard-tinned rake and/or shovel to dig up as many of the roots as you can. Burn or dispose of the roots.
Watch carefully for new dune grass plants to emerge. When they do, spray their leaves immediately with Roundup. Wait 7 days and then dig down and remove the roots of the dune grass which has been killed by the Roundup.
Be vigilant. Continue to spray all new dune grass growth with Roundup and then dig up the roots. Ridding your yard of dune grass can be a two-season project.