Coupled modeling of sediment-laden flows based on local-time-step approach

doi:10.3785/j.issn.1008-973X.2019.04.015

Journal of ZheJiang University (Engineering Science)

2019, Vol. 53

Issue (4): 743-752 DOI: 10.3785/j.issn.1008-973X.2019.04.015

Coupled modeling of sediment-laden flows based on local-time-step approach

Peng HU(

),Jian-jian HAN,Yun-long LEI

Ocean College, Zhejiang University, Zhoushan 316021, China

Download:

HTML

PDF(1555KB) HTML
Export: BibTeX | EndNote (RIS)

Abstract

A new coupled model for sediment-laden flows was established with high computational efficiency by using the local-time-step (LTS) technology (i.e., using locally allowable maximum time step for variable updating at each cell). The governing equations that fully consider the interactions among the water flow, sediment transport and bed topography, were discretized by the finite volume method on unstructured triangular meshes. The inter-cell numerical fluxes were estimated by the HLLC approximate Riemann solver. The numerical case studies of dam-break floods over mobile bed suggested a reduction of the computational cost by 68% when adopting an appropriate LTS level. Engineering application of the model to the Taipingkou waterway of the Changjiang River led to a 92% reduction in the computational cost without losing quantitative accuracy.

Key words： coupled model for sediment-laden flows finite volume method computational efficiency local-time-step

Received: 29 January 2018 Published: 28 March 2019

CLC:

TV 142

	Service
	E-mail this article
	Add to my bookshelf
	Add to citation manager
	E-mail Alert
	RSS
	Articles by authors
	Peng HU
	Jian-jian HAN
	Yun-long LEI

Cite this article:

Peng HU,Jian-jian HAN,Yun-long LEI. Coupled modeling of sediment-laden flows based on local-time-step approach. Journal of ZheJiang University (Engineering Science), 2019, 53(4): 743-752.

URL:

http://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2019.04.015 OR http://www.zjujournals.com/eng/Y2019/V53/I4/743

基于局部分级时间步长方法的水沙耦合数学模拟

基于局部时间步长（LTS）技术（即在每个计算网格采用局部允许的最大时间步长），建立新的水沙数学模型，提高计算效率. 用非结构三角形网格离散计算区域，采用充分反映水-沙-床相互作用的平面二维完整控制方程组，利用有限体积法求解控制方程，用HLLC近似黎曼算子估算界面数值通量. 对动床溃坝算例的计算表明，当选取合适的局部时间步长级数时，计算效率明显提高（节省计算时间幅度达到68%），精度满足要求. 长江中游太平口水道的工程应用表明，该模型能够在保证精度的前提下，节省高达92%的计算时间.

关键词： 水沙耦合模型, 有限体积法, 计算效率, 局部时间步长

Fig.1 Program flow chart for local-time-step approach

Fig.2 Water depth profiles at 64 s for simulating dam-break flow over fixed bed

Tab.1 Computational cost and quantitative accuracy for simulating dam-break flow over fixed beds using local-time-step

Fig.3 Plan view of UCL dam-break experimental configuration

Fig.4 Computed (using different L) and measured water level hydrographs against time at six gauges for UCL case

Fig.5 Computed (using different L) and measured bed profiles at CS1 and CS2 for UCL case

Tab.2 Computational cost and quantitative accuracy for simulating dam-break flow over mobile beds using LTS

Fig.6 Location of Taipingkou waterway and meshes

Fig.7 Boundary conditions for Taipingkou waterway

Fig.8 Computed (with different L) water depth for Taipingkou waterway

Fig.9 Computed (with different L) and measured bed erosion and deposition patter for Taipingkou waterway

Tab.3 Computational cost and quantitative accuracy for simulating fluvial process of Taipingkou waterway using LTS


[1]	王嘉松, 倪汉根, 金生二维溃坝问题的高分辨率数值模拟[J]. 上海交通大学学报, 1999, 33 (10): 1213- 1216 WANG Jia-song, NI Han-gen, JIN Sheng High-resolution numerical simulations for two-dimensional dam-break problems[J]. Journal of Shanghai Jiaotong University, 1999, 33 (10): 1213- 1216 doi: 10.3321/j.issn:1006-2467.1999.10.006

[2]	HOU J, LIANG Q, ZHANG H, et al An efficient unstructured MUSCL scheme for solving the 2D shallow water equations[J]. Environmental Modelling and Software, 2015, 66 (C): 131- 152

[3]	YUE Z, LIU H, LI Y, et al A well-balanced and fully coupled noncapacity model for dam-break flooding[J]. Mathematical Problems in Engineering, 2015, (3): 1- 13

[4]	许栋, 徐彬, DAVID P, et al 基于GPU并行计算的浅水波运动数值模拟[J]. 计算力学学报, 2016, 33 (01): 114- 121 XU Dong, XU Bin, DAVID P, et al Numerical simulation of shallow water motion based on parallel computation using GPU[J]. Chinese Journal of Computational Mechanics, 2016, 33 (01): 114- 121

[5]	贺治国, 吴钢锋, 王振宇, 等台风暴雨影响区域的溃坝洪水演进数值计算[J]. 浙江大学学报: 工学版, 2010, 44 (08): 1589- 1596 HE Zhi-guo, WU Gang-feng, WANG Zhen-yu, et al Numerical simulation for dam-break flood in hurricane-prone regions[J]. Journal of Zhejiang University: Engineering Science, 2010, 44 (08): 1589- 1596

[6]	冉启华, 吴秀山, 贺治国, 等冰湖溃决模式对下游洪水过程的影响[J]. 清华大学学报: 自然科学版, 2014, 54 (08): 1049- 1056 RAN Qi-hua, WU Xiu-shan, HE Zhi-guo, et al Impact of glacial lake breach mechanism on downstream flood progress[J]. Journal of Tsinghua University: Science and Technology, 2014, 54 (08): 1049- 1056

[7]	吴钢锋, 贺治国, 刘国华基于守恒稳定格式的二维坡面降雨动力波洪水模型[J]. 浙江大学学报: 工学版, 2014, 48 (03): 514- 520 WU Gang-feng, HE Zhi-guo, LIU Guo-hua Well-balanced two-dimensional dynamic wave model for rainfall-included overland flood[J]. Journal of Zhejiang University: Engineering Science, 2014, 48 (03): 514- 520

[8]	房克照, 尹晶, 孙家文, 等基于二维浅水方程的滑坡体兴波数值模型[J]. 水科学进展, 2017, 28 (01): 96- 105 FANG Ke-zhao, YIN Jing, SUN Jia-wen, et al A numerical model for landslide-generated waves based on two-dimensional shallow water equations[J]. Advances in Water Science, 2017, 28 (01): 96- 105

[9]	于普兵, 潘存鸿, 谢亚力二维风暴潮实时预报模型及其在杭州湾的应用[J]. 水动力学研究与进展A辑, 2011, 26 (06): 747- 756 YU Pu-bing, PAN Cun-hong, XIE Ya-li 2-dimesional real time forecasting model for storm tides and its application in Hangzhou Bay[J]. Chinese Journal of Hydrodynamics, 2011, 26 (06): 747- 756 doi: 10.3969/j.issn1000-4874.2011.06.014

[10]	TORO E F. Shock-capturing methods for free-surface shallow flows [M]. Chichester: Wiley, 2001.

[11]	ZHOU J G, CAUSON D M, MINGHAM C G, et al The surface gradient method for the treatment of source terms in the shallow-water equations[J]. Journal of Computational Physics, 2001, 168 (1): 1- 25 doi: 10.1006/jcph.2000.6670

[12]	BEGNUDELLI L, SANDERS B F Unstructured grid finite volume algorithm for shallow-water flow and transport with wetting and drying[J]. Journal of Hydraulic Engineering, 2006, 132 (4): 371- 384 doi: 10.1061/(ASCE)0733-9429(2006)132:4(371)

[13]	LIANG Q, BORTHWICK A G L Adaptive quadtree simulation of shallow flows with wet dry fronts over complex topography[J]. Computers and Fluids, 2009, 38 (2): 221- 234 doi: 10.1016/j.compfluid.2008.02.008

[14]	CAO Z X, PENDER G, CARLING P Shallow water hydrodynamic models for hypercon-centrated sediment-laden floods over erodible bed[J]. Advances in Water Resources, 2006, 29 (4): 546- 557 doi: 10.1016/j.advwatres.2005.06.011

[15]	CAO Z X, PENDER G, WALLIS S, et al Computational dam-break hydraulics over erodible sediment bed[J]. Journal of Hydraulic Engineering, 2004, 130 (7): 689- 703 doi: 10.1061/(ASCE)0733-9429(2004)130:7(689)

[16]	CANESTRELLI A, SIVIGLIA A, DUMBSER M, et al Well-balanced high-order centred schemes for non-conservative hyperbolic systems. applications to shallow water equations with fixed and mobile bed[J]. Advances in Water Resources, 2009, 32 (6): 834- 844 doi: 10.1016/j.advwatres.2009.02.006

[17]	HENG B C P, SANDERS G C, SCOTT C F Modeling overland flow and soil erosion on nonuniform hillslopes: a finite volume scheme[J]. Water Resources Research, 2009, 45 (5): 641- 648

[18]	LI W, VRIEND H J, WANG Z, et al Morphological modeling using a fully coupled, total variation diminishing upwind-biased centered scheme[J]. Water Resources Research, 2013, 49 (6): 3547- 3565 doi: 10.1002/wrcr.20138

[19]	HU P, CAO Z X, PENDER G Fully coupled mathematical modeling of turbidity currents over erodible bed[J]. Advances in Water Resources, 2009, 32 (1): 1- 15 doi: 10.1016/j.advwatres.2008.07.018

[20]	HU P, CAO Z X, PENDER G Well-balanced two-dimensional coupled modeling of submarine turbidity currents[J]. Maritime Engineering, 2012, 165 (4): 169- 188 doi: 10.1680/maen.2010.12

[21]	HU P, CAO Z X, PENDER G, et al Numerical modelling of riverbed grain size stratigraphic evolution[J]. International Journal of Sediment Research, 2014, 29 (3): 329- 343 doi: 10.1016/S1001-6279(14)60048-2

[22]	SANDERS B F Integration of a shallow water model with a local time step[J]. Journal of Hydraulic Research, 2008, 46 (4): 466- 475 doi: 10.3826/jhr.2008.3243

[23]	KESSERWANI G, LIANG Q RKDG2 shallow-water solver on non-uniform grids with local time steps: application to 1D and 2D hydrodynamics[J]. Applied Mathematical Modelling, 2015, 39 (3/4): 1317- 1340

[24]	DAZZI S, MARANZONI A, MIGNOSA P Local time stepping applied to mixed flow modelling[J]. Journal of Hydraulic Research, 2016, 54 (2): 1- 13

[25]	OSHER S, SANDERS R Numerical approximations to nonlinear conservation laws with locally varying time and space grids[J]. Mathematics of Computation, 1983, 41 (164): 321- 336 doi: 10.1090/S0025-5718-1983-0717689-8

[26]	DAWSON C, KIRBY R High resolution schemes for conservation laws with locally varying time steps[J]. Society for Industrial and Applied Mathematics, 2001, 22 (6): 2256- 2281

[27]	CROSSLEY A J, WRIGHT N G, WHITLOW C D Local time stepping for modeling open channel flows[J]. Journal of Hydraulic of Engineering, 2003, 129 (6): 455- 462 doi: 10.1061/(ASCE)0733-9429(2003)129:6(455)

[28]	CROSSLEY A J, WRIGHT N G Time accurate local time stepping for the unsteady shallow water equations[J]. International Journal for Numerical Methods in Fluids, 2005, 48 (7): 775- 799 doi: 10.1002/(ISSN)1097-0363

[29]	王巍. 浅水方程有限体积法的并行计算研究 [D]. 上海: 上海交通大学, 2008. WANG Wei. Development and applications of parallel algorithm with shallow wave equation [D]. Shanghai: Shanghai Jiao Tong University, 2008.

[30]	周洋, 张景新浅水方程的并行化求解[J]. 力学季刊, 2013, 34 (4): 607- 613 ZHOU Yang, ZHANG Jing-xin Parallel simulation of shallow water flow[J]. Chinese Quarterly of Mechanics, 2013, 34 (4): 607- 613 doi: 10.3969/j.issn.0254-0053.2013.04.013

[31]	DAZZI S, VACONDIO R, PALU A D, et al A local time stepping algorithm for GPU-accelerated 2D shallow water models[J]. Advances in Water Resources, 2017, 111 (1): 274- 288

[32]	QIAN H, CAO Z, PENDER G, et al Well-balanced numerical modelling of non-uniform sediment transport in alluvial rivers[J]. International Journal of Sediment Reasearch, 2015, 30 (2): 117- 130 doi: 10.1016/j.ijsrc.2015.03.002

[33]	WU W. Computational river dynamics [M]. London: Taylor & Francis, 2007.

[34]	张瑞瑾. 河流泥沙动力学 [M]. 北京: 水利电力出版社, 1989.

[35]	SPINEWINE B, ZECH Y Small-scale laboratory dam-break waves on movable beds[J]. Journal of Hydraulic Research, 2007, 45 (Suppl.1): 73- 86

[1]	Shuo HUANG,Shuang-qiang WANG,Peng WANG,Gui-yong ZHANG. Comparative study of application of smoothed point interpolation method in fluid-structure interactions[J]. Journal of ZheJiang University (Engineering Science), 2020, 54(8): 1645-1654.

[2]	Wei LI,Ji-yu ZOU,Peng HU. Urban flood simulation based on porosity and local time step[J]. Journal of ZheJiang University (Engineering Science), 2020, 54(3): 614-622.

[3]	WU Gang-feng,HE Zhi-guo,LIU Guo-hua. Well-balanced two-dimensional dynamic wave model for rainfall-induced overland flood[J]. Journal of ZheJiang University (Engineering Science), 2014, 48(3): 514-520.

[4]	CHEN Yi-fan, CHENG Wei-ping, JIANG Jian-qun, QIAN Jing-lin. Simulation of two-dimensional flow field in mountain rivers under cascade hydraulic structures[J]. Journal of ZheJiang University (Engineering Science), 2013, 47(11): 1945-1950.

Viewed

Full text

Abstract

Cited

Shared

Discussed