2D Zero-Inertia Model for Solution of Overland Flow Problems in Flexible Meshes

AbstractA 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 b...

[1]  V. Ponce.  Generalized diffusion wave equation with inertial effects , 1990 .

[2]  Ben C. Yen,et al.  On noninertia wave versus diffusion wave in flood routing , 2001 .

[3]  A. M. Wasantha Lal,et al.  Performance Comparison of Overland Flow Algorithms , 1998 .

[4]  Jin Chen,et al.  Global land cover mapping at 30 m resolution: A POK-based operational approach , 2015 .

[5]  A. M. Wasantha Lal,et al.  Weighted Implicit Finite-Volume Model for Overland Flow , 1998 .

[6]  Qiuhua Liang,et al.  A positivity-preserving zero-inertia model for flood simulation , 2011 .

[7]  Pilar García-Navarro,et al.  Diffusive-Wave Based Hydrologic-Hydraulic Model with Sediment Transport. I: Model Development , 2012 .

[8]  C. Yang,et al.  Estimating overland flow erosion capacity using unit stream power. , 2009 .

[9]  Almasi S. Maguya,et al.  Adaptive algorithm for large scale dtm interpolation from lidar data for forestry applications in steep forested terrain , 2013 .

[10]  Jayantha Obeysekera,et al.  A Wetland Simulation Module for the MODFLOW Ground Water Model , 1998 .

[11]  Henk A. van der Vorst,et al.  Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems , 1992, SIAM J. Sci. Comput..

[12]  Murugesu Sivapalan,et al.  A generalized, non-linear, diffusion wave equation: theoretical development and application , 1997 .

[13]  R. Moussa,et al.  Criteria for the choice of flood-routing methods in natural channels , 1996 .

[14]  A. Roth,et al.  The shuttle radar topography mission—a new class of digital elevation models acquired by spaceborne radar , 2003 .

[15]  Pilar García-Navarro,et al.  A numerical model for the flooding and drying of irregular domains , 2002 .

[16]  Misganu Debella-Gilo,et al.  Spatial prediction of soil classes using digital terrain analysis and multinomial logistic regression modeling integrated in GIS: Examples from Vestfold County, Norway , 2009 .

[17]  Christina W. Tsai.  Applicability of Kinematic, Noninertia, and Quasi-Steady Dynamic Wave Models to Unsteady Flow Routing , 2003 .

[18]  Jerónimo Puertas,et al.  Experimental validation of two-dimensional depth-averaged models for forecasting rainfall-runoff from precipitation data in urban areas , 2010 .

[19]  Pierre Y. Julien,et al.  Two-dimensional simulations of extreme floods on a large watershed , 2007 .

[20]  Venkatesh M. Merwade,et al.  GIS techniques for creating river terrain models for hydrodynamic modeling and flood inundation mapping , 2008, Environ. Model. Softw..

[21]  Yuhong He,et al.  An object-based approach to delineate wetlands across landscapes of varied disturbance with high spatial resolution satellite imagery ☆ , 2015 .

[22]  LAND-USE IMPACT ON WATERSHED RESPONSE: THE INTEGRATION OF TWO-DIMENSIONAL HYDROLOGICAL MODELLING AND GEOGRAPHICAL INFORMATION SYSTEMS , 1996 .

[23]  Ben Chie Yen,et al.  Diffusion-Wave Flood Routing in Channel Networks , 1981 .

[24]  Javier Murillo,et al.  An optimized GPU implementation of a 2D free surface simulation model on unstructured meshes , 2014, Adv. Eng. Softw..

[25]  Javier Murillo,et al.  Influence of mesh structure on 2D full shallow water equations and SCS Curve Number simulation of rainfall/runoff events , 2012 .

[26]  Javier Murillo,et al.  Weak solutions for partial differential equations with source terms: Application to the shallow water equations , 2010, J. Comput. Phys..

[27]  Victor Miguel Ponce.  Diffusion Wave Modeling of Catchment Dynamics , 1986 .

[28]  Fred J. Molz,et al.  A 2-D, diffusion-based, wetland flow model , 1997 .

[29]  Q. Liang,et al.  Numerical resolution of well-balanced shallow water equations with complex source terms , 2009 .

[30]  L. M Gomes Pereira,et al.  Suitability of laser data for deriving geographical information: A case study in the context of management of fluvial zones , 1999 .

[31]  Yousef Saad,et al.  ILUT: A dual threshold incomplete LU factorization , 1994, Numer. Linear Algebra Appl..

[32]  Pilar García-Navarro,et al.  Zero mass error using unsteady wetting–drying conditions in shallow flows over dry irregular topography , 2004 .

[33]  Pilar García-Navarro,et al.  Efficient construction of high‐resolution TVD conservative schemes for equations with source terms: application to shallow water flows , 2001 .