I wish to test the numerical m
 

I wish to test the numerical methods in OpenFOAM on a well known hyperbolic test-problem, namely the p-system:
[v u]_t + [-u A*v^-gamma]_x = 0
I have written a piece of code that solves this in 1D, using the OpenFOAM space-discretization-operator div. The time-stepping is made with a 2:nd order TVD Runge-Kutta. My question is the following:
The convection-specific schemes calculate the interpolation based on the flux of the flow velocity. What should I consider as the flow velocity here?

I have solved the "shallow-wat
 

I have solved the "shallow-water" equations in various ways but never the "p-system". In the former the choice of flux variable is obvious but in the later it is definitely not obvious. What physical problem can the "p-system" be applied to?

The p-system is a model for is
 

The p-system is a model for isentropic (=constant entropy) or polytropic gas given in a Lagrangian coordinate system.
v is the specific volume i.e. 1/rho and u is the velocity, and p=A*v^-gamma is the pressure (A>0 and gamma=1.4 typically for air).
I have defined both v and u as volScalarFields, and by this choice I can use the linear interpolation scheme. However since I want to solve a Riemann problem I want to test all the different TVD methods already implemented in OpenFOAM. What is the easiest solution to this?

If u is the velocity then you
 

If u is the velocity then you should construct a flux from it somehow, ideally by constructing a pressure equation and getting the flux from that but if that is not appropriate then by linear interpolation.