Two phase flow solid-fluid in river beds
 

Hello everyone... i would appreciate some guidance on this subject

To solve the unsteady nature of this flow "title", i have to account for the transient part of the hydrodynamic model, the actual simplified model i have "previously implemented" is a two coupled equations system, one for the hydrodynamics "fluid phase" and the other is derived from Exner equation "solid phase", the model is coupled. In the fluid phase, the change of velocity in time is not taken into account "transients", my task at this stage is to account for it, and solve it numerically.

Note: the previous model is solved by FD method

My questions:
To account for the transient state "unsteady flow", the hydrodynamic equation has to be in conservative form but it is not....?
Since this is meant to simulate a shock "torrential flows", finite volume is a must, because it captures the discontinuities, is it possible to combine with FD, or the whole system has to be implemented in Finite volume method.

and please excuse me if i add another question:
There are two times scales each one associated with its phase flow "solid and fluid", choosing the finer scale is appropriate to capture fluid evolution i suppose. correct !


Thanks a lot for your discussion/inputs