A non-uniform efficient grid type for GPU-parallel Shallow Water Equations models

A GPU-parallel numerical model for the solution of the 2D Shallow Water Equations, based on a novel type of grid called Block-Uniform Quadtree (BUQ), is presented. BUQ grids are based on a data structure which allows to exploit the computational capability of GPUs with minimum overheads, while discretizing the domain with non-uniform resolution. Different cases have been simulated in order to assess the efficiency of the BUQ grids. Theoretical and laboratory tests demonstrate that speed-ups of up to one order of magnitude can be achieved in comparison with uniform Cartesian grids. In the simulation of a hypothetical flood event induced by a levee breach in a real 83źkm long river reach, with maximum resolution of 5źm, a ratio of physical to computational time of about 12 was obtained, opening scenarios of quasi real-time 2D simulations in large domains, still retaining a high resolution where necessary. Shallow Water Equations parallel numerical scheme suitable for GPU.Novel Block-Uniform Quadtree (BUQ) grid-type, exploiting the computational capability of GPUs with non-uniform resolution.Very large domain can be simulated (38źkm river reach) with high resolution (2źm).Speed-up of one order of magnitude is achieved, in comparison with Uniform resolution Cartesian Grids.High ratio between physical and computational time which enables real-time simulations.

[1]  E. Toro.  Riemann Solvers and Numerical Methods for Fluid Dynamics , 1997 .

[2]  G. J. M. Copeland,et al.  Adaptive hierarchical grid model of water-borne pollutant dispersion , 2000 .

[3]  M. Vázquez-Cendón.  Improved Treatment of Source Terms in Upwind Schemes for the Shallow Water Equations in Channels with Irregular Geometry , 1999 .

[4]  Two dimensional modeling of rapidly varying flows by finite volume schemes , 2004 .

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

[6]  Brett F. Sanders,et al.  Impact of Limiters on Accuracy of High-Resolution Flow and Transport Models , 2006 .

[7]  Qiuhua Liang,et al.  Shallow flow simulation on dynamically adaptive cut cell quadtree grids , 2007 .

[8]  Pierfranco Costabile,et al.  Enhancing river model set-up for 2-D dynamic flood modelling , 2015, Environ. Model. Softw..

[9]  Pilar García-Navarro,et al.  Reconstruction of 2D river beds by appropriate interpolation of 1D cross-sectional information for flood simulation , 2014, Environ. Model. Softw..

[10]  Qiuhua Liang,et al.  Simulation of dam‐ and dyke‐break hydrodynamics on dynamically adaptive quadtree grids , 2004 .

[11]  Valerio Caleffi,et al.  Finite volume method for simulating extreme flood events in natural channels , 2003 .

[12]  B. Sanders,et al.  Unstructured grid finite-volume algorithm for shallow-water flow and scalar transport with wetting and drying , 2006 .

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

[14]  L. Feyen,et al.  Ensemble flood risk assessment in Europe under high end climate scenarios , 2015 .

[15]  Vincenzo Casulli,et al.  Semi-implicit finite difference methods for the two-dimensional shallow water equation , 1990 .

[16]  Stephen M. Longshaw,et al.  DualSPHysics: Open-source parallel CFD solver based on Smoothed Particle Hydrodynamics (SPH) , 2015, Comput. Phys. Commun..

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

[18]  Joseph H. A. Guillaume,et al.  Characterising performance of environmental models , 2013, Environ. Model. Softw..

[19]  Javier Murillo,et al.  An efficient GPU implementation for a faster simulation of unsteady bed-load transport , 2016 .

[20]  Masayuki Fujihara,et al.  Adaptive Q-tree Godunov-type scheme for shallow water equations , 2001 .

[21]  Paolo Mignosa,et al.  Simulation of the January 2014 flood on the Secchia River using a fast and high-resolution 2D parallel shallow-water numerical scheme , 2015, Natural Hazards.

[22]  Knut-Andreas Lie,et al.  Efficient GPU-Implementation of Adaptive Mesh Refinement for the Shallow-Water Equations , 2014, Journal of Scientific Computing.

[23]  Marc de la Asunción,et al.  Efficient GPU implementation of a two waves TVD-WAF method for the two-dimensional one layer shallow water system on structured meshes , 2013 .

[24]  B. Rogers,et al.  SPH Modeling of Shallow Flow with Open Boundaries for Practical Flood Simulation , 2012 .

[25]  Qiuhua Liang,et al.  A structured but non‐uniform Cartesian grid‐based model for the shallow water equations , 2011 .

[26]  Qiuhua Liang,et al.  Adaptive quadtree simulation of shallow flows with wet-dry fronts over complex topography , 2009 .

[27]  Javier Murillo,et al.  An efficient solution for hazardous geophysical flows simulation using GPUs , 2015, Comput. Geosci..

[28]  E. Penning-Rowsell,et al.  Flood risk assessments at different spatial scales , 2015, Mitigation and Adaptation Strategies for Global Change.

[29]  William G. Gray,et al.  A wave equation model for finite element tidal computations , 1979 .

[30]  Sandra Soares Frazao,et al.  Dam-break Flow through Sharp Bends - Physical Model and 2D Boltzmann Model Validation , 1999 .

[31]  Deborah Greaves,et al.  Hierarchical tree-based finite element mesh generation , 1999 .

[32]  Qiuhua Liang,et al.  Flood Inundation Modeling with an Adaptive Quadtree Grid Shallow Water Equation Solver , 2008 .

[33]  Mustafa S. Altinakar,et al.  Efficient shallow water simulations on GPUs: Implementation, visualization, verification, and validation , 2012 .

[34]  G. Petrova,et al.  A SECOND-ORDER WELL-BALANCED POSITIVITY PRESERVING CENTRAL-UPWIND SCHEME FOR THE SAINT-VENANT SYSTEM ∗ , 2007 .

[35]  Flávio A. Sousa,et al.  Simulation of surface fire fronts using fireLib and GPUs , 2012, Environ. Model. Softw..

[36]  Hyunuk An,et al.  An accurate multidimensional limiter on quadtree grids for shallow water flow simulation , 2014 .

[37]  Brett F. Sanders,et al.  ParBreZo: A parallel, unstructured grid, Godunov-type, shallow-water code for high-resolution flood inundation modeling at the regional scale , 2010 .

[38]  Steven J. Burian,et al.  Assessment of GPU computational enhancement to a 2D flood model , 2011, Environ. Model. Softw..

[39]  Yves Zech,et al.  Dam Break in Channels with 90° Bend , 2002 .

[40]  P. Mignosa,et al.  Local time stepping applied to mixed flow modelling , 2016 .

[41]  Javier Murillo,et al.  GPU implementation of the 2D shallow water equations for the simulation of rainfall/runoff events , 2015, Environmental Earth Sciences.

[42]  Alessandro Dal Palù,et al.  GPU-enhanced Finite Volume Shallow Water solver for fast flood simulations , 2014, Environ. Model. Softw..