I am working on the discrete theory of compressible fluids dynamics, i.e., numerically solving and simulating the compressible fluids , we are interested in the way using discrete exterior calculus, my question is: Is there any work on the discrete theory (especially using discrete exterior calculus) of compressible fluids? 



The discrete theory of compressible fluids dynamics
There's unpublished work by Gay-Balmaz and Pavlov, *Variational Discretization of Compressible Fluids*, described [here](http://d-pavlov.com/resources/Research_Statement.pdf), with an instructive summary of the difficulties involved in extending the discrete theory from incompressible to compressible fluids.


