Density ratio

I'd like some help with my basic understanding of density depenent modelling and the use of the density ratio parameter.

My understanding is that the density ratio, which is defined for elements by the user, affects the freshwater head assigned at flow boundary conditions (e.g. type 1).  h_fw = h_sw + density ratio * (h_sw - z)

...and the density ratio is dependent on the difference between reference density (the background fluid density in the model) and the maximum density assigned at the boundary condition (e.g. at a sea water boundary).  density ratio = (max density - reference density) / reference density.  e.g. at C = 0 and 35,000 g/m3, density ratio = (1035 kg/m3 - 1000 kg/m3)/1000 kg/m3 = 0.035

Question 1: How does density ratio affect the computation of density driven flow inside the model?

Question 2: If the concentration (and therefore density) at the boundary condition is required to increase during the model run, is the density ratio assigned to the elements still valid?  Or does the density ratio need to change through time to reflect the new maximum density in the model?

Question 3: What would you suggest as an approach for modelling density flow where the concentration and density at the main boundary is increasing over time?

Question 4: In unconfined (free and movable) problems, h = z at slice 1.  Does h_fw = h_sw on any Type 1 head boundaries on slice 1?

Appreciate the help...

Q1: density-coupled flow is an unstable process similar to flow in the vadose zone.  Highly nonlinear problem: requires fine mesh and small times steps.  I believe quads are best.

Q2: Perhaps choose an average ratio.  You could treat the ratio as a calibration parameter in which case its calibration sensitivity would be nice to know

Q3: see 2

Q4: I don't know

As an update to this, and to those who are interested, this was clarified by the WASY support team.

In cases of a changing concentration BC, there is a difference between the global density ratio parameter and the density ratio applied for that BC.  The global parameter should remain fixed and relates to the reference and maximum concentrations which are set by the user in the global transport settings (C0 and Cs). 

When density dependent modelling is active, the Darcy flow equation includes a buoyancy term K* ([(Rho - Rho0)/Rho0] * grad(z))

In FEFLOW, the density term is determined by concentration by:
[(Rho - Rho0)/Rho0] = density ratio * ([C - C0]/[Cs-C0])

So the buoyancy term in the Darcy eqn becomes K* (density ratio * ([C - C0]/[Cs-C0]) * grad(z))


When you define a saltwater head BC is FEFLOW, it uses the global density ratio by default to set the equivalent freshwater head, using:
h_fw = h_sw + density ratio * (h_sw - z)  where z is the node elevation.

This assumes C at this boundary = Cs.  However, when C is not Cs, h_fw needs to be calculated using a different density ratio according to [(Rho - Rho0)/Rho0] ... where Rho is the BC density and Rho0 is the reference density, usually the minimum density in the model.

So this pretty much requires an IFM...

And it is not advisable to use free and movable surfaces for 3D density problems... So it's confined mode only.

Lots of horizontal and vertical discretisation is a given...

Hi Blair,

one little correction: Excluding free&moveable still leaves the options for phreatic and unsaturated - besides confined.

Best regards,
Peter