2D Zero-Inertia Model for Solution of Overland Flow Problems in Flexible Meshes
Publication: Journal of Hydrologic Engineering
Volume 21, Issue 11
Abstract
A study of the efficiency of a zero-inertia model (ZI) for two-dimensional (2D) overland flow simulation is presented in this work. An upwind numerical scheme is used for the spatial discretization in the frame of finite-volume methods and an implicit formulation is chosen to avoid numerical instability. The scheme is applied in both structured and unstructured meshes, focusing in the latter ones due to their good adaptability. The ZI equation has a nonlinear character; hence, a linearization is required in the implicit procedure. This is carried out by means of Picard iterations method as a previous step to the system matrix resolution, characteristic of implicit techniques. The BiConjugate Gradient Stabilized (BiCGStab) method combined with sparse storage strategies is selected for the system resolution. A dual-threshold incomplete lower upper factorization (ILUT) is chosen as matrix preconditioner. Computational efficiency of the implicit temporal discretization for ZI model is explored under both steady and unsteady flow conditions by comparing the CPU times against the explicit version of the same model.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The present work was partially funded by the Aragón Government through the Fondo Social Europeo.
References
Akan, A. (2006). Open channel hydraulics, Elsevier.
Akan, A., and Yen, B. (1977). “A non-linear diffusion-wave model for unsteady open channel flow.” Proc., 17th IAHR Congress, Vol. 2, International Association for Hydraulic Research, Delft, Netherlands, 181–190.
Akan, A., and Yen, B. (1981). “Diffusion-wave flood routing in channel networks.” J. Hydraul. Div., 107(6), 719–732.
Brufau, P., García-Navarro, P., and Vázquez-Cendón, M. E. (2004). “Zero mass error using unsteady wetting-drying conditions in shallow flows over dry irregular topography.” Int. J. Numer. Methods Fluids, 45(10), 1047–1082.
Brufau, P., Vázquez-Cendón, M. E., and García-Navarro, P. (2002). “A numerical model for the flooding and drying of irregular domains.” Int. J. Numer. Methods Fluids, 39(3), 247–275.
Burden, R., and Faires, J. (2010). Numerical analysis, 9th Ed., Brooks/Cole, Cengage Learning, Boston.
Burguete, J., and García-Navarro, P. (2001). “Efficient construction of high-resolution TVD conservative schemes for equation with source terms: Application to shallow water flows.” Int. J. Numer. Methods Fluids, 37(2), 209–248.
Caviedes-Voullième, D., García-Navarro, P., and Murillo, J. (2012). “Influence of mesh structure on 2D full shallow water equations and SCS Curve Number simulation of rainfall/runoff events.” J. Hydrol., 448-449, 39–59.
Cea, L., Garrido, M., and Puertas, J. (2010). “Experimental validation of two-dimensional depth-averaged models for forecasting rainfall-runoff from precipitation data in urban areas.” J. Hydrol., 382(1-4), 88–102.
Chen, J., et al. (2015). “Global land cover mapping at 30 m resolution: A POK-based operational approach.” ISPRS J. Photogramm. Remote Sens., 103, 7–27.
Debella-Gilo, M., and Etzelmüller, B. (2009). “Spatial prediction of soil classes using digital terrain analysis and multinomial logistic regression modeling integrated in GIS: Examples from Vestfold County, Norway.” CATENA, 77(1), 8–18.
Doe, W., Saghafian, B., and Julien, P. (1996). “Land-use impact on watershed response: The integration of two-dimensional hydrological modelling and geographical information systems.” Hydrol. Process., 10(11), 1503–1511.
England, J., Jr., Velleux, M., and Julien, P. (2007). “Two-dimensional simulations of extreme floods on a large watershed.” J. Hydrol., 347(1-2), 229–241.
Feng, K., and Molz, F. (1997). “A 2-D, diffusion-based, wetland flow model.” J. Hydrol., 196(1-4), 230–250.
Hirsch, C. (2007). Numerical computation of external and internal flows, 2nd Ed., Butterworth-Heinemann, Oxford.
Lacasta, A., Morales-Hernández, M., Murillo, J., and García-Navarro, P. (2014). “An optimized GPU implementation of a 2D free surface simulation model on unstructured meshes.” Adv. Eng. Software, 78, 1–15.
Lal, A. W. (1998a). “Performance comparison of overland flow.” J. Hydraul. Eng., 342–349.
Lal, A. W. (1998b). “Weighted implicit finite-volume model for overland flow.” J. Hydraul. Eng., 941–950.
Liang, Q., and Marche, F. (2009). “Numerical resolution of well-balanced shallow water equations with complex source terms.” Adv. Water Resour., 32(6), 873–884.
López-Barrera, D., García-Navarro, P., Brufau, P., and Burguete, J. (2012). “Diffusive-wave based hydrologic-hydraulic model with sediment transport. I: Model development.” J. Hydrol. Eng., 1093–1104.
Maguya, A. S., Junttila, V., and Kauranne, T. (2013). “Adaptive algorithm for large scale dtm interpolation from lidar data for forestry applications in steep forested terrain.” ISPRS J. Photogramm. Remote Sens., 85, 74–83.
Merwade, V., Cook, A., and Coonrod, J. (2008). “GIS techniques for creating river terrain models for hydrodynamic modeling and flood inundation mapping.” Environ. Model. Software, 23(10-11), 1300–1311.
Moussa, R., and Bocquillon, C. (1996). “Criteria for the choice of flood-routing methods in natural channels.” J. Hydrol., 186(1-4), 1–30.
Moussa, R., and Marche, F. (2009). “Numerical resolution of well-balanced shallow water equations with complex source terms.” Adv. Water Resour., 32(6), 873–884.
Mui, A., He, Y., and Weng, Q. (2015). “An object-based approach to delineate wetlands across landscapes of varied disturbance with high spatial resolution satellite imagery.” ISPRS J. Photogramm. Remote Sens., 109, 30–46.
Murillo, J., and García-Navarro, P. (2010). “Weak solutions for partial differential equations with source terms: Application to the shallow water equations.” J. Comput. Phys., 229, 4327–4368.
Pereira, L. G., and Wicherson, R. (1999). “Suitability of laser data for deriving geographical information: A case study in the context of management of fluvial zones.” ISPRS J. Photogr. Remote Sens., 54(2-3), 105–114.
Ponce, V. (1986). “Diffusion wave modeling of catchment dynamics.” J. Hydraul. Eng., 716–727.
Ponce, V. (1990). “Generalized diffusion wave equation with inertial effects.” Water Resour. Res., 26(5), 1099–1101.
Rabus, B., Eineder, M., Roth, A., and Bamler, R. (2003). “The shuttle radar topography mission—A new class of digital elevation models acquired by spaceborne radar.” ISPRS J. Photogramm. Remote Sens., 57(4), 241–262.
Restrepo, J., Montoya, A., and Obeysekera, J. (1998). “Simulation module for the MODFLOW ground water model.” Ground Water, 36(5), 764–770.
Saad, Y. (1994). “ILUT: A dual threshold incomplete LU factorization.” Numer. Linear Algebra Appl., 1(4), 387–402.
Shih, H.-M., and Yang, C. T. (2009). “Estimating overland flow erosion capacity using unit stream power.” Int. J. Sediment Res., 24(1), 46–62.
Sivapalan, M., Bates, B., and Larsen, J. (1997). “A generalized, non-linear, diffusion wave equation: Theoretical development and application.” J. Hydrol., 192(1-4), 1–16.
Te Chow, V., Maidment, D., and Mays, L. (1988). Applied hydrology, McGraw-Hill, New York.
Tsai, C. (2003). “Applicability of kinematic, noninertia, and quasi-steady dynamic wave models to unsteady flow routing.” J. Hydraul. Eng., 613–627.
van der Vorst, H. (1992). “BI-CGSTAB—A fast and smoothly converging variant of BI-CG for the solution of nonsymmetric linear-systems.” SIAM J. Sci. Stat. Comput., 13(2), 631–644.
Vreugdenhil, C. (1994). Numerical methods for shallow water flow, Kluwer Academic, Dordrecht, Netherlands.
Wang, Y., Liang, Q., Kesserwani, G., and Hall, J. W. (2011). “A positivity-preserving zero-inertia model for flood simulation.” Comput. Fluids, 46(1), 505–511.
Yen, B., and Tsai, C. W. S. (2001). “On noninertia wave versus diffusion wave in flood routing.” J. Hydrol., 244(1–2), 97–104.
Information & Authors
Information
Published In
Journal of Hydrologic Engineering
Volume 21 • Issue 11 • November 2016
Copyright
© 2016 American Society of Civil Engineers.
History
Received: Nov 18, 2015
Accepted: Apr 15, 2016
Published online: Jun 23, 2016
Published in print: Nov 1, 2016
Discussion open until: Nov 23, 2016
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.