Efficient shallow water simulations on GPUs: Implementation, visualization, verification, and validation

Abstract In this paper, we present an efficient implementation of a state-of-the-art high-resolution explicit scheme for the shallow water equations on graphics processing units. The selected scheme is well-balanced, supports dry states, and is particularly suitable for implementation on graphics processing units. We verify and validate our implementation, and show that use of efficient single precision hardware is sufficiently accurate for real-world simulations. Our framework further supports real-time visualization with both photorealistic and non-photorealistic display of the physical quantities. We present performance results showing that we can accurately simulate the first 4000 s of the Malpasset dam break case in 27 s using over 480,000 cells ( dx  =  dy  = 15 m), in which our simulator runs at an average of 530 megacells per second.

[1]  Miguel Lastra,et al.  Simulation of shallow-water systems using graphics processing units , 2009, Math. Comput. Simul..

[2]  Jostein R. Natvig,et al.  Visual simulation of shallow-water waves , 2005, Simul. Model. Pract. Theory.

[3]  José Miguel Mantas,et al.  Programming CUDA-Based GPUs to Simulate Two-Layer Shallow Water Flows , 2010, Euro-Par.

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

[5]  Xinya Ying,et al.  MODELING FLOOD INUNDATION DUE TO DAM AND LEVEE BREACH , 2005 .

[6]  Uri C. Weiser,et al.  Proceedings of the 37th annual international symposium on Computer architecture , 2010, ISCA 2010.

[7]  Pradeep Dubey,et al.  Debunking the 100X GPU vs. CPU myth: an evaluation of throughput computing on CPU and GPU , 2010, ISCA.

[8]  Takayuki Aoki,et al.  Real-Time Tsunami Simulation on Multi-node GPU Cluster , 2009 .

[9]  John D. Owens,et al.  GPU Computing , 2008, Proceedings of the IEEE.

[10]  R. LeVeque.  Finite Volume Methods for Hyperbolic Problems: Characteristics and Riemann Problems for Linear Hyperbolic Equations , 2002 .

[11]  Doron Levy,et al.  CENTRAL-UPWIND SCHEMES FOR THE SAINT-VENANT SYSTEM , 2002 .

[12]  Knut-Andreas Lie,et al.  How to Solve Systems of Conservation Laws Numerically Using the Graphics Processor as a High-Performance Computational Engine , 2007, Geometric Modelling, Numerical Simulation, and Optimization.

[13]  Hans Werner Meuer,et al.  Top500 Supercomputer Sites , 1997 .

[14]  Timothy C. Warburton,et al.  Nodal discontinuous Galerkin methods on graphics processors , 2009, J. Comput. Phys..

[15]  Peng Wang,et al.  Adaptive mesh fluid simulations on GPU , 2009, 0910.5547.

[16]  Knut-Andreas Lie,et al.  Unconditionally Stable Splitting Methods for the Shallow Water Equations , 1999, Bit Numerical Mathematics.

[17]  E. Toro.  Shock-Capturing Methods for Free-Surface Shallow Flows , 2001 .

[18]  Jostein R. Natvig,et al.  Simulation and visualization of the Saint-Venant system using GPUs , 2010, Comput. Vis. Sci..

[19]  Christopher Dyken,et al.  State-of-the-art in heterogeneous computing , 2010, Sci. Program..

[20]  Valerio Caleffi,et al.  Case Study: Malpasset Dam-Break Simulation using a Two-Dimensional Finite Volume Method , 2002 .

[21]  Chi-Wang Shu.  Total-variation-diminishing time discretizations , 1988 .

[22]  J. Hervouet,et al.  Malpasset dam-break revisited with two-dimensional computations , 1999 .

[23]  Konstantinos I. Karantasis,et al.  Acceleration of a Finite-Difference WENO Scheme for Large-Scale Simulations on Many-Core Architectures , 2010 .

[24]  Chin-Chuan Han,et al.  A GPU-Based Simulation of Tsunami Propagation and Inundation , 2009, ICA3PP.

[25]  W. Thacker.  Some exact solutions to the nonlinear shallow-water wave equations , 1981, Journal of Fluid Mechanics.

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

[27]  Sandra Soares Frazao,et al.  Dam-break test cases summary 4th CADAM meeting , 1999 .

[28]  José Miguel Mantas,et al.  Simulation of one-layer shallow water systems on multicore and CUDA architectures , 2010, The Journal of Supercomputing.

[29]  Manmohan Singh,et al.  Moving boundary shallow water flow above parabolic bottom topography , 2006 .

[30]  Jostein R. Natvig,et al.  Solving the Euler Equations on Graphics Processing Units , 2006, International Conference on Computational Science.

[31]  Alexander Kurganov,et al.  Semidiscrete Central-Upwind Schemes for Hyperbolic Conservation Laws and Hamilton-Jacobi Equations , 2001, SIAM J. Sci. Comput..

[32]  Graham Pullan,et al.  Acceleration of a two-dimensional Euler flow solver using commodity graphics hardware , 2007 .

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

[34]  Graham Pullan,et al.  Acceleration of a 3D Euler solver using commodity graphics hardware , 2008 .