[dune-fem] compressible two phase flow

[Andrea Capolei]

Hi all,
I would like to solve a two phase compressible flow using dune-fem. The equations I'm using are in
pressure/saturation form.

After finite volume spatial discretization I have the following system of ODEs to solve:

d/dt C(u(t)) = F(u(t)) + Q,

u = [P;S] // vector of pressures and saturations in each block
C = phi * rho(P) * S // Concentrations
F = fluxes
Q = source terms

I want to use the implicit euler method, then in each time step and in each iteration of the Newton solver
I need to solve:

[d/du C - dt d/du F] du = Residual


Unfortunately from dune-fem tutorials I only found how to solve problems in the normal form
d/dt u(t) = F(u(t)) + Q

i.e. (Id: identity matrix)
[Id - dt d/du F] du = Residual


How could I solve my problem with dune-fem? Do you have any example?
I was thinking to add another  operator "C_operator" in the odesolver and then change the newton function. But I'm not sure if it's a good idea.
I would like to maintain compatibility with the dune-fem interface.


Thanks,
    Andrea


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