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Zhang, Ting; Peng, Ling; Feng, Ping

Evaluation of a 3D unstructured-mesh finite element model for dam-break floods. (English) Zbl 1390.76382

Comput. Fluids 160, 64-77 (2018).
Summary: This paper aims to comprehensively understand a 3D model for simulating dam-break floods through three test cases. The advantages and characteristics of this model are evaluated from different perspectives. Firstly, vertical inertial is considered in the 3D model. In the existing 1D and 2D flooding models, vertical inertia is usually ignored, resulting in unreliable results in high vertical inertia situations. A circular dam break case was designed and widely used for testing 2D models. Here, it has been adopted to test the 3D model. Evident difference has been observed when compared with 2D modelling results. In order to reduce the vertical inertial in this case, we scaled the vertical size by 1:100, while kept the original horizontal size, then amplified the results according to the Froude number scaling rule. The results of the scaled model is very close to 2D modelling results. Therefore, the difference between the 3D and 2D modelling results are mainly caused by the vertical inertia. Thus it can be seen that 3D modelling techniques are needed when vertical inertia is not negligible. Secondly, the use of unstructured mesh makes this model more powerful in operating with complex topography, which is very important in real-world application. Five similar cases with different topography demonstrated that the complexity of topography affects the numerical solution process directly. However, this 3D model has powerful ability in utilizing very complex terrain. Thirdly, sensitivity of the model to the thickness of the artificial thin layer in dry areas (d0) and mesh resolution (\(\Delta x\)) have been analysed with a realistic dike-break flooding case. Smaller d0 produces more realistic results but costs more computational time. The model is more sensitive to mesh resolution when the terrain is more complex. Therefore, a multi-scale mesh with high-resolution in areas with complex terrain and low-resolution in flat regions is a good choice for this model. Also, trade-offs between modelling precision and efficiency should be considered when choosing a proper value of d0 and mesh resolution.

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
76D05 Navier-Stokes equations for incompressible viscous fluids

Keywords:

dam-break flood; three-dimensional modelling; unstructured mesh; wetting and drying; vertical inertia

Software:

Gmsh
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Full Text: DOI

References:

[1] Cotter, C. J.; Ham, D. A.; Pain, C. C., A mixed discontinuous/continuous finite element pair for shallow-water Ocean modelling, Ocean Modell, 26, 1, 86-90, (2009)
[2] Du, J.; Fang, F.; Pain, C. C.; Navon, I. M.; Zhu, J.; Ham, D. A., Rreduced-order unstructured mesh modelling applied to 2d and 3d fluid flow, Comput Math Appl, 65, 362-379, (2013) · Zbl 1319.76026
[3] Fewtrell, T. J.; Bates, P. D.; Horritt, M.; Hunter, N. M., Evaluating the effect of scale in flood inundation modelling in urban environments, Hydrol Process, 22, 26, 5107-5118, (2008)
[4] Funke, S. W.; Pain, C. C.; Kramer, S. C.; Piggott, M. D., A wetting and drying algorithm with a combined pressure/free-surface formulation for non-hydrostatic models, Adv Water Resour, 34, 11, 1483-1495, (2011)
[5] Geuzaine, C.; Remacle, J. F., Gmsh: a 3-d finite element mesh generator with built- in pre- and post-processing facilities, Int J Numer Methods Eng, 79, 11, 1309-1331, (2009) · Zbl 1176.74181
[6] Haltas, I.; Elci, S.; Tayfur, G., Numerical simulation of flood wave propagation in two-dimensions in densely populated urban areas due to dam break, Water Resour Manage, 30, 15, 1-23, (2016)
[7] Horritt, M. S.; Bates, P. D., Evaluation of 1-d and 2-d numerical models for predicting river flood inundation, J Hydrol, 268, 1-4, 87-99, (2002)
[8] Hsu, M. H.; Chen, S. H.; Chang, T. J., Inundation simulation for urban drainage basin with storm sewer system, J Hydrol, 234, 1, 21-37, (2000)
[9] Hunter, N. M.; Bates, P. D.; Horritt, M. S.; Wilson, M. D., Simple spatially-distributed models for predicting flood inundation: a review, Geomorphology, 90, 3, 208-225, (2007)
[10] Hunter, N. M.; Bates, P. D.; Neelz, S.; Pender, G., Benchmarking 2d hydraulic models for urban flooding, Proc ICE-Water Manag, 161, 1, 13-30, (2008)
[11] Kim, B.; Sanders, B. F., Dam-break flood model uncertainty assessment: case study of extreme flooding with multiple dam failures in gangneung, south Korea, J Hyduraul Eng, 142, 5, 05016002, (2016)
[12] Lane, S. N.; Bradbrook, K. F.; Richards, K. S.; Biron, P. A.; Roy, A. G., The application of computational fluid dynamics to natural river channels: three-dimensional versus two-dimensional approaches, Geomorphology, 29, 1-20, (1999)
[13] Liang, Q.; Borthwick, A. G.L.; Stelling, G., Simulation of dam- and dyke-break hydrodynamics on dynamically adaptive quadtree grids, Int J Numer Methods Fluids, 46, 2, 127-162, (2004) · Zbl 1060.76590
[14] Liang, Q.; Du, G.; Hall, J. W.; Borthwick, A. G.L., Flood inundation modelling with an adaptive quadtree grid shallow water equation solver, J Hydraul Eng, 134, 11, 1603-1610, (2008)
[15] Marks, K.; Bates, P., Integration of high-resolution topographic data with floodplain flow models, Hydrol Process, 14, 11-12, 2109-2122, (2000)
[16] Mark, O.; Weesakul, S.; Apirumanekul, C.; Aroonnet, S. B.; Djordjevic, S., Potential and limitations of 1d modelling of urban flooding, J Hydrol, 299, 3, 284-299, (2004)
[17] Schumann, G. J.; Bates, P. D.; Neal, J. C.; Andreadis, K. M., Technology: fight floods on a global scale, Nature, 507, 7491, 169-170, (2014)
[18] Schubert, J. E.; Sanders, B. F.; Smith, M. J.; Wright, N. G., Unstructured mesh generation and landcover-based resistance for hydrodynamic modelling of urban flooding, Adv Water Resour, 31, 12, 1603-1621, (2008)
[19] Seyoum, S. D.; Vojinovic, Z.; Price, R. K.; Weesakul, S., Coupled 1d and noninertia 2d flood inundation model for simulation of urban flooding, J Hydraul Eng, 138, 1, 23-34, (2011)
[20] Toro EF. Shock Capturing Methods for Free-Surface Shallow Flows. John Wiley and Sons Ltd, 2001.; Toro EF. Shock Capturing Methods for Free-Surface Shallow Flows. John Wiley and Sons Ltd, 2001. · Zbl 0996.76003
[21] Yin, L.; Zhu, J.; Zhang, X.; Li, Y., Visual analysis and simulation of dam-break flood spatiotemporal process in a network environment, Environ Earth Sci, 74, 10, 7133-7146, (2015)
[22] Zhang, T.; Feng, P.; Maksimović, C.; Bates, P. D., Application of a three-dimensional unstructured-mesh finite-element flooding model and comparison with two-dimensional approaches, Water Resour Manage, 30, 823-841, (2016)
[23] Zhu, J.; Yin, L.; Wang, J.; Zhang, H., Dam-break flood routing simulation and scale effect analysis based on virtual geographic environment, IEEE J Sel Top Appl Earth Obs Remote Sens, 8, 1, 105-113, (2015)
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