Posted Fri, 17 Oct 2014 13:01:54 GMT by Roman Sigut
Hi all,

I am trying to construct numerical model (fem attached) describing seawater intrusion in the coastal area. My model shows some senseless values, especially high negative values.
Mesh is constructed with help of Advancing front type of mesh generator, no obtuse triangles occurs and the mesh respects the Delunay criterion. Total amount of element in one slice is 9428 and model is divided into 10 layers (11 slices). In the model, two boundary conditions (BC) are set: 1st BC and 2nd BC. 1st BC is set in coastal area (0 m) and in north part, which is opposite site to coastal area (15 m), east and west part of the model is described with 2nd BC (0 m/d).
Concerning mass transport boundary, there is only 1st BC set (35000 mg/l) in coastal area. A 0 mg/l initial mass concentration has been assigned.

Any idea would be great.


Posted Mon, 03 Nov 2014 17:26:58 GMT by adacovsk
You're probably using large timestep values and it is oscillating. You might either want to try reducing the mesh size around the mass transport boundary or reducing the initial timestepping/growth factor more. Over a long time though, the oscillation should go away. I always set the growth factor to be <2.
Posted Wed, 19 Nov 2014 18:55:30 GMT by Björn Kaiser
Negative concentrations may be considered as a „self-diagnostic“ indicating weaknesses in the model setup.

There are several ways on dealing with negative concentrations. These different ways may be categorized in adaption and smoothing techniques. Whether adaption or smoothing techniques are preferred depends very much on the study area, individual model settings and also on the question you want to answer.

During the first attempts, I suggest prioritizing adaption techniques rather than smoothing techniques. If all attempts fail, you could try to use smoothing techniques.

Here are some (general) questions I would try to answer before I switch to smoothing techniques:

1. Is the mesh fine enough? A fine mesh is required especially at sharp interfaces of primary variables (e.g. heads or freshwater-saltwater interface) and in areas where sharp contrasts in physical rock properties characterize the hydrogeological setting.

2. Does the mesh contain bad shaped elements? Try to use the maximum interior angle of triangles instead of the Delaunay criterion violations. You may improve the mesh using mesh smoothing techniques from the Mesh Geometry Toolbar.

3. What temporal discretization are you using? I guess you use an automatic predictor-corrector time stepping scheme. That’s fine. But sometimes additional constraints by means of a growth factor between subsequent time-steps or/and of a maximum time-step size may improve your model.

4. Fully implicit schemes are generally more stable than (semi-)implicit schemes. Accordingly, you may switch from a second order-accurate semi-implicit scheme (AB/TR) to a fully implicit first-order accurate (FE/BE) scheme.

5. What error norm are you using? The maximum error norm represents a more stringent criterion compared to integral error norms given the fact that the maximum error norm focuses more on local effects within the model. In this regard you may also change the error tolerance.

Finally, if all these settings still do not give rise to the desired result or if (for instance) the mesh would contain too many elements, which exceeds the handling of your computational resources, you may think about adopting Upwinding to stabilize the numerical solution artificially. Upwinding techniques smooth steep gradients of computational findings by adding (artificial) numerical dispersion. In other words, you change the physics of your system in order to reach a numerically stable solution. Therefore, I always would be cautious when dealing with Upwinding.

You may also think about accepting negative concentrations to a certain degree. Criteria to assess whether or not a concentration is acceptable could be the magnitude of the concentration or the spatial location where the negative concentration occurs.
Posted Thu, 20 Nov 2014 08:37:13 GMT by Roman Sigut
thank you very much for your answers. I will try to use yours advices in my model and let you know whether it works or not.

Thanks, Roman

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