Free Surface Flows and Cavities Emergence by a Flux-corrected Finite Element Method

Advanced simulation of free surface natural flows, and of combined free surface/pressurized flows in hydraulic structures, requires a proper numerical approach for the dynamics of interfaces, avoiding spurious residuals during interface propagation. Errors due to mass and momentum imbalances during propagation are associated with the method employed in cells where interface belongs, as in the case of partially wet computational elements, and in the interface capture technique.

In recent years we introduced a finite element model to simulate shallow flows with dry fronts (e.g.[1]), extending the formulation to flows coupled with erodible–non erodible sediment interfaces [2]. The method is developed by integrating a high order continuous finite element procedure with a conservative sign-preserving correction. Corrected continuous model has an inherent solution for the motion of interfaces, and does not need extensive modifications to compute flooding and evolutionary beds.

The incorporation of relevant sources could produce high order conservation errors in the solution by standard flux correction procedure. In this work we present an extended conservative finite element method based on flux limiters with improved conservation properties after correction. We introduce applications of the procedure to severe frictional flows, such as experiments of dam–break flow type problems over combined erodible/non–erodible beds.

Besides, air cavities propagation in ducts is a stringent problem of air/water interface propagation. In this case, the interface is a combination of regions where transition air-water is well defined and zones where a diffuse transition between both phases appears, frequently due to the a bore formation. To complete our work, we extend the finite element model to the capture of cavities (in two and three dimensional problems). We illustrate the suitability of the model for experiments of air/water propagation and cavity emergence in ducts, both in terms of error norms and in terms of enclosed volume conservation error.

Acknowledgements: This research is supported by MICIIN Grant #BIA-2015-64994-P (MINECO/FEDER).

REFERENCES

[1] P.Ortiz, “Shallow water flows over flooding areas by a flux-corrected finite element method”, Journal of Hydraulic Research, 52, 2, 241-252 (2014).

[2] P. Ortiz, J. Anguita, M. Riveiro, “Free surface flows over partially erodible beds by a continuous finite element method”, Environ. Earth Sci., 74, 7357–7330 (2015).