Posted Wed, 25 Jul 2007 17:47:02 GMT by Simon

Lots to ask....

Scratching my head here. I think my problems are with the modelling rather than being conceptual, but if you can help me out either way I'll be happy.

The problem.. 3D, steady state, saturated, unconfined with phreatic surface with the default constraints for the phreatic surface set for 'falling dry' 'touching top surface'.

Model boundaries, pretty much fixed head all the way around. I know I have too much water coming in to my system, but I'm limited to working from a previous regional model thats been okayed.

I have also lots of streams, sub surface and surface drains which I'm required to model explicitly, for water balances etc. I figured 1D discrete elements might help me out otherwise it would all get a bit messy.

So, Ive set my transfer boundary conditions as you would, stage for streams, elevation for surface drains, and below elevation for the others..

Transfer boundary constraints for minimum heads are set appropriately for streams/drains.

My feature element are set along my transfer boundary conditions with conductance, transfer in/out etc set, I hope correctly (Im assuming that flow is Darcy along my (porous) rivers with a conductance == 1m/s).

As anticipated from the boundary conditions I have to work with my model heads are way to high ~10m above ground surface. This is pre sensitivity analysis, which is likely to be futile, but I have some questions regarding my base case.

In summary, my questions are.

1) Do the default constraints (in my case unconstrained touching top surface) during the iterative phase and at final solution ignore, say, any maximum boundary constraints you may have set on your transfer conditions? I ask this as the  option to constrain your heads to ground level by applying the dirichlet conditions over the model domain seem to supercede any internal boundary condition. ie you don't get any flow in/out your tranfer boundaries even if the head distruibution suggest you should.

2) Do transfer conditions, in the instance of using the 1D feature elements, only need to be applied themselves in 1D along the defined discrete element conditions? They would seem to work.

3) I'm a little uncertain as to the best way to represent a good approximation for a stream/drain using the linear elements. Is a high K value of 1m/s high enough, or would the maximum you can get away with in the model be more appropriate?

4) Convergence in my model seems highly sensitive to the 1D elements. Specifically with regard to transfer in/out values (the lower the better), conductance and cross sectional area and not discretisation. This appears to be in the case where I have high head gradients. I thought increasing conductance and increasing cross sectional area would be the way forward, but it seems the converse is true. I confess to not understanding the reason why, and that the attachment of 1D elements to a finite element grid is new to me. Im assuming that the transfer conditions apply directly to the 1D element nodes, and also that the modelled heads do too. Its the simulation of flow along the 1D element, in addition to whatever is going on in the element below that I do not fully understand. I've tried the white papers, but Im non the wiser.

5) Is the simulation of a cutoff wall using a low K vertical quadrilateral fracture element a suitable approximation? For a single layer do I need to apply this condition to an upper and lower slice?



Posted Wed, 01 Aug 2007 08:34:44 GMT by Simon
Answers to some of my questions...

The idea of my modelling approach was to use the 1D linear elements simply to allow a linear designation of transfer boundary conditions, and not really to model the actual flow within the streams. So my questions regardnig the correct way to simulate flow in the 1d eleemnts are unnecesaary. It is possible to use the discrete elements in this fashion, but this requires a reinterpretation of the input required for the linear 1D elements. For example flux in the 1D element is calculated using the x-sectional area of the stream/drain. In my case this cross sectional area is actually the area occupied by the stream bed. You also have to account for the transmissivity of the 1D element by appropriately adjusting the conductivity.
I found this approach highly sensitive in the model, and it will require more of my time to determine f this approach really is consistent. I decided to scrap this approach.

Perhaps WASY could add a different option to the 1D elements such that the additional equations associated with the 1D elements explicitly permit the definition of linear stream/drains in this fashion? It would be extremeley useful to be able to define streams/drains in 1D with associated in/out parameters in 1D for complex drain/stream systems, in the sense that flow in the 1D element is unimportant, its rather the flux in/out of the model that we want to represent.

No you can't use a 2D fracture element to represent a cut off wall. This is buried deep in the reference manuals. Material properties should be round about the properties of surounding elements or have higher conductivity.

I think that the application of constraints, such as those to limit the water level to ground level by aplying dirichlet conditions over the whole model should not supercede any internal boundary conditions. My internal transfer conditions were necessarily below ground level and consequently became redundant. I could set transfer condition across my whole model with transfer in/out values that conform to reasonable recharge values across the domain to constrain water leveles to round about ground surface, but this seems particularly over constraied. It also means that explicitly defining measure properties of say river bed conductance becomes oh so more tricky with the adjacent model wide transfer conditions.

WASY support suggested that a linear tranfer boundary condition could be defined with transfer conditions applied in the vertical sense. ie add another layer beneath with the same transfer condition. This is good lateral (vertical!) thinking. Of course this still means that I have to define my transfer in/out values on the top surface for the elements.

Some information on 1D element from WASY support


- 1D discrete elements are additional connections between existing nodes
- there is no resistance between the nodes of the 'background' mesh and the discrete elements, both share the same nodes
- in a 1D discrete element, for example using Darcy's law, the flow is calculated by Q = -k * A * deltah/deltax, where A is the cross-sectional area and deltah is the head difference between the two nodes, deltax the distance
- 1D discrete elements are always calculated as fully saturated
- in unsaturated parts of the model are turned off automatically
- the transfer rate of a discrete element is used in case of a transfer condition directly on the element for calculating the boundary flow into/from the discrete element
- the transfer rate of a discrete element does not control the flow between the discrete element and the 'background' mesh

the 1D discrete elements are always calculated as fully saturated, so their shape is always the same. In a steady-state case, you can take that as width * water depth, where the water depth does not change throughout the model run. Please note that the 1D elements are always perfectly connected to the mesh. So in your case there won't be any clogging layer in the river. The transfer rates are only used in case that you have transfer boundary conditions on the nodes of your discrete elements. Compressibility won't have a major influence. Manning might be more appropriate for a river than Darcy, but will lead to a non-linear behavior of the conductivity


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