Similar articles

Abstract: solute transport simulations are important in water pollution events. This paper introduces a finite volume Godunov-type model for solving a 4×4 matrix form of the hyperbolic conservation laws consisting of 2D shallow water equations and transport equations. The model adopts the Harten-Lax-van Leer-contact (HLLC)-approximate Riemann solution to calculate the cell interface fluxes. It can deal well with the changes in the dry and wet interfaces in an actual complex terrain, and it has a strong shock-wave capturing ability. Using monotonic upstream-centred scheme for conservation laws (MUSCL) linear reconstruction with finite slope and the Runge-Kutta time integration method can achieve second-order accuracy. At the same time, the introduction of graphics processing unit (GPU)-accelerated computing technology greatly increases the computing speed. The model is validated against multiple benchmarks, and the results are in good agreement with analytical solutions and other published numerical predictions. The third test case uses the GPU and central processing unit (CPU) calculation models which take 3.865 s and 13.865 s, respectively, indicating that the GPU calculation model can increase the calculation speed by 3.6 times. In the fourth test case, comparing the numerical model calculated by GPU with the traditional numerical model calculated by CPU, the calculation efficiencies of the numerical model calculated by GPU under different resolution grids are 9.8–44.6 times higher than those by CPU. Therefore, it has better potential than previous models for large-scale simulation of solute transport in water pollution incidents. It can provide a reliable theoretical basis and strong data support in the rapid assessment and early warning of water pollution accidents.

基于图形处理器加速的急变流条件下溶质输移的稳健数值模型

[1]Aidun CK, Clausen JR, 2010. Lattice-Boltzmann method for complex flows. Annual Review of Fluid Mechanics, 42(1):439-472.

[2]Audusse E, Bristeau MO, 2003. Transport of pollutant in shallow water a two time steps kinetic method. ESAIM: M2AN, 37(2):389-416.

[3]Barredo JI, 2007. Major flood disasters in Europe: 1950-2005. Natural Hazards, 42(1):125-148.

[4]Bayazıt Y, Koç C, Bakış R, 2021. Urbanization impacts on flash urban floods in Bodrum Province, Turkey. Hydrological Sciences Journal, 66(1):118-133.

[5]Begnudelli L, Sanders BF, 2006. Unstructured grid finite-volume algorithm for shallow-water flow and scalar transport with wetting and drying. Journal of Hydraulic Engineering, 132(4):371-384.

[6]Benkhaldoun F, Elmahi I, Seaı¨d M, 2007. Well-balanced finite volume schemes for pollutant transport by shallow water equations on unstructured meshes. Journal of Computational Physics, 226(1):180-203.

[7]Bi S, Zhou JZ, Cheng SS, et al., 2013. A high-precision two-dimensional flow-transport coupled model based on Godunov’s schemes. Advances in Water Science, 24(5):706-714 (in Chinese).

[8]Cao Y, Ye YT, Liang LL, et al., 2019. High efficient and accurate simulation of pollutant transport in torrential flow based on adaptive grid method. Journal of Hydraulic Engineering, 50(3):388-398 (in Chinese).

[9]Chen CY, Lu TH, Yang YF, et al., 2021. Toxicokinetic/ toxicodynamic-based risk assessment of freshwater fish health posed by microplastics at environmentally relevant concentrations. Science of the Total Environment, 756: 144013.

[10]Dong J, 2020. A robust central scheme for the shallow water flows with an abrupt topography based on modified hydrostatic reconstructions. Mathematical Methods in the Applied Sciences, 43(15):9024-9045.

[11]Duarte HDO, Droguett EL, Araújo M, et al., 2013. Quantitative ecological risk assessment of industrial accidents: the case of oil ship transportation in the coastal tropical area of northeastern Brazil. Human and Ecological Risk Assessment: An International Journal, 19(6):1457-1476.

[12]Fraccarollo L, Toro EF, 1995. Experimental and numerical assessment of the shallow water model for two-dimensional dam-break type problems. Journal of Hydraulic Research, 33(6):843-864.

[13]Harten A, Lax PD, van Leer B, 1983. On upstream differencing and Godunov-type schemes for hyperbolic conservation laws. SIAM Review, 25(1):35-61.

[14]Hou JM, Simons F, Hinkelmann R, 2012. Improved total variation diminishing schemes for advection simulation on arbitrary grids. International Journal for Numerical Methods in Fluids, 70(3):359-382.

[15]Hou JM, Simons F, Hinkelmann R, 2013a. A new TVD method for advection simulation on 2D unstructured grids. International Journal for Numerical Methods in Fluids, 71(10):1260-1281.

[16]Hou JM, Simons F, Mahgoub M, et al., 2013b. A robust well-balanced model on unstructured grids for shallow water flows with wetting and drying over complex topography. Computer Methods in Applied Mechanics and Engineering, 257:126-149.

[17]Hou JM, Liang QH, Zhang HB, et al., 2014. Multislope MUSCL method applied to solve shallow water equations. Computers & Mathematics with Applications, 68(12):2012-2027.

[18]Hou JM, Liang QH, Li ZB, et al., 2015. Numerical error control for second-order explicit TVD scheme with limiters in advection simulation. Computers & Mathematics with Applications, 70(9):2197-2209.

[19]Hou JM, Wang R, Liang QH, et al., 2018a. Efficient surface water flow simulation on static Cartesian grid with local refinement according to key topographic features. Computers & Fluids, 176:117-134.

[20]Hou JM, Wang T, Li P, et al., 2018b. An implicit friction source term treatment for overland flow simulation using shallow water flow model. Journal of Hydrology, 564:357-366.

[21]Hou JM, Kang YD, Hu CH, et al., 2020. A GPU-based numerical model coupling hydrodynamical and morphological processes. International Journal of Sediment Research, 35(4):386-394.

[22]Kachiashvili K, Gordeziani D, Lazarov R, et al., 2007. Modeling and simulation of pollutants transport in rivers. Applied Mathematical Modelling, 31(7):1371-1396.

[23]Kawahara M, Umetsu T, 1986. Finite element method for moving boundary problems in river flow. International Journal for Numerical Methods in Fluids, 6(6):365-386.

[24]Kong J, Xin P, Shen CJ, et al., 2013. A high-resolution method for the depth-integrated solute transport equation based on an unstructured mesh. Environmental Modelling & Software, 40:109-127.

[25]La Rocca M, Montessori A, Prestininzi P, et al., 2015. A multispeed discrete Boltzmann model for transcritical 2D shallow water flows. Journal of Computational Physics, 284:117-132.

[26]La Rocca M, Miliani S, Prestininzi P, 2020. Discrete Boltzmann numerical simulation of simplified urban flooding configurations caused by dam break. Frontiers in Earth Science, 8:346.

[27]Li YP, Wei J, Gao XM, et al., 2018. Turbulent bursting and sediment resuspension in hyper-eutrophic Lake Taihu, China. Journal of Hydrology, 565:581-588.

[28]Liang QH, 2010. A well-balanced and non-negative numerical scheme for solving the integrated shallow water and solute transport equations. Communications in Computational Physics, 7(5):1049-1075.

[29]Liang QH, Xia XL, Hou JM, 2016. Catchment-scale high-resolution flash flood simulation using the GPU-based technology. Procedia Engineering, 154:975-981.

[30]Liu RX, 2011. Simulation of water transferring impact on the water quality in Danjiangkou reservoir of the south to north water diversion middle line project. Journal of Basic Science and Engineering, 19(S1):193-200 (in Chinese).

[31]Liu WH, Chen RQ, Qiu RF, et al., 2020. Generalized form of interpolation-supplemented lattice Boltzmann method for computational aeroacoustics. Journal of Zhejiang University (Engineering Science), 54(8):1637-1644 (in Chinese).

[32]Murillo J, García-Navarro P, Burguete J, 2009. Conservative numerical simulation of multi-component transport in two-dimensional unsteady shallow water flow. Journal of Computational Physics, 228(15):5539-5573.

[33]Petti M, Bosa S, 2007. Accurate shock-capturing finite volume method for advection-dominated flow and pollution transport. Computers & Fluids, 36(2):455-466.

[34]Roccati A, Faccini F, Luino F, et al., 2019. Heavy rainfall triggering shallow landslides: a susceptibility assessment by a GIS-approach in a Ligurian Apennine catchment (Italy). Water, 11(3):605.

[35]Shao JR, Wu SQ, Zhou J, et al., 2012. High-accuracy numerical simulation of 2D transport problems. Advances in Water Science, 23(3):383-389 (in Chinese).

[36]Smith LS, Liang QH, 2013. Towards a generalised GPU/CPU shallow-flow modelling tool. Computers & Fluids, 88: 334-343.

[37]Song LX, Yang F, Hu XZ, et al., 2014. A coupled mathematical model for two-dimensional flow-transport simulation in tidal river network. Advances in Water Science, 25(4):550-559 (in Chinese).

[38]Tang CY, Li YP, Jiang P, et al., 2015. A coupled modeling approach to predict water quality in Lake Taihu, China: linkage to climate change projections. Journal of Freshwater Ecology, 30(1):59-73.

[39]Tao T, Lu YJ, Fu X, et al., 2012. Identification of sources of pollution and contamination in water distribution networks based on pattern recognition. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 13(7):559-570.

[40]Toro EF, 2001. Shock-capturing Methods for Free-surface Shallow Flow. John Wiley & Sons, Ltd., Chichester, UK.

[41]Venturi S, Francesco SD, Geier M, et al., 2021. Modelling flood events with a cumulant CO lattice Boltzmann shallow water model. Natural Hazards, 105(2):1815-1834.

[42]Wang ZW, Cheng WP, 2002. Analysis of ecological mechanism of urban flood and waterlog—research based mainly on Hangzhou City. Journal of Zhejiang University (Engineering Science), 36(5):582-587 (in Chinese).

[43]Zhang LL, Liang QH, Wang YL, et al., 2015. A robust coupled model for solute transport driven by severe flow conditions. Journal of Hydro-environment Research, 9(1):49-60.

[44]Zhang WJ, Lin XY, Su XS, 2010. Transport and fate modeling of nitrobenzene in groundwater after the Songhua River pollution accident. Journal of Environmental Management, 91(11):2378-2384.

[45]Zhang WW, 2011. Measuring the value of water quality improvements in Lake Tai, China. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 12(9):710-719.

[46]Zhao Y, Nan J, Cui FY, et al., 2007. Water quality forecast through application of BP neural network at Yuqiao reservoir. Journal of Zhejiang University-SCIENCE A, 8(9):1482-1487.