Application of Graphics Processing Units for Self-Consistent Modelling of Shallow Water Dynamics and Sediment Transport
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Application of Graphics Processing Units for Self-Consistent Modelling of Shallow Water Dynamics and Sediment Transport S. S. Khrapov1* and A. V. Khoperskov1** (Submitted by Vl. V. Voevodin) 1
Volgograd State University, Volgograd, 400062 Russia
Received March 1, 2020; revised April 15, 2020; accepted April 20, 2020
Abstract—In this paper, we describe a numerical algorithm for the self-consistent simulations of surface water and sediment dynamics. The method is based on the original Lagrangian-Eulerian CSPH-TVD approach for solving the Saint-Venant and Exner equations, taking into account the physical factors essential for the understanding of the shallow water and surface soil layer motions, including complex terrain structure and its evolution due to sediment transport. Additional Exner equation for sediment transport has been used for the numerical CSPH-TVD scheme stability criteria definition. By using OpenMP-CUDA and GPUDirect technologies for hybrid computing systems (supercomputers) with several graphic coprocessors (GPUs) interacting with each other via the PCI-E/NVLINK interface we also develop a parallel numerical algorithm for the CSPHTVD method. The developed parallel version of the algorithm demonstrates high efficiency for various configurations of Nvidia Tesla CPU + GPU computing systems. In particular, maximal speed up is 1800 for a system with four C2070 GPUs compare to the serial version for the CPU. The calculation time on the GPU V100 (Volta architecture) is reduced by 95 times compared to the GPU C2070 (Fermi architecture). DOI: 10.1134/S1995080220080089 Keywords and phrases: parallel computing, GPUs, numerical methods, shallow water model.
1. INTRODUCTION Modelling of unsteady flows of the surface fluid requires the calculation of movable flow boundaries [1] where the presence of sediment transport complicates this problem because the boundaries between the fluid and sediment may not coincide. Another complicating factor, in addition to the heterogeneity of the bottom topography b(x, y), is the heterogeneity of soil characteristics (e.g., porosity, particle sizes). A detailed analysis of various models of sediment transport can be found in [2]. Usually, the mathematical model of a shallow water dynamics is based on hyperbolic equations for which Godunovtype solvers are often used [3]. One such solver used by many authors is the Harten–Lax–Leer (HLL) [4] scheme, and another approach is based on Roe’s approximate solver [5]. Nowadays, another state-ofthe-arm approach for modelling sediment transport by water flow is the discrete least-squares meshless method [6]. Recently advantages of the architecture of modern GPUs have been successfully used to solve a wide range of mathematical problems [7–13] thus making usage of the parallel computing on GPUs even more topical for a broad range of academical and applied problems. In this work, we discuss a combined SPH-TVD method for the numerical integration of the Saint-Venant and Exner equations which was proposed previously in our works [14–15]. In this paper
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