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Volume 7, Issue 2
A High-Order Numerical Method to Study Three-Dimensional Hydrodynamics in a Natural River

Luyu Shen, Changgen Lu, Weiguo Wu & Shifeng Xue

Adv. Appl. Math. Mech., 7 (2015), pp. 180-195.

Published online: 2018-05

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  • Abstract

A high-order numerical method for three-dimensional hydrodynamics is presented. The present method applies high-order compact schemes in space and a Runge-Kutta scheme in time to solve the Reynolds-averaged Navier-Stokes equations with the $k-ϵ$ turbulence model in an orthogonal curvilinear coordinate system. In addition, a two-dimensional equation is derived from the depth-averaged momentum equations to predict the water level. The proposed method is first validated by its application to simulate flow in a $180^◦$ curved laboratory flume. It is found that the simulated results agree with measurements and are better than those from SIMPLEC algorithm. Then the method is applied to study three-dimensional hydrodynamics in a natural river, and the simulated results are in accordance with measurements.


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@Article{AAMM-7-180, author = {Luyu and Shen and and 10059 and and Luyu Shen and Changgen and Lu and and 10060 and and Changgen Lu and Weiguo and Wu and and 10061 and and Weiguo Wu and Shifeng and Xue and and 10062 and and Shifeng Xue}, title = {A High-Order Numerical Method to Study Three-Dimensional Hydrodynamics in a Natural River}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2018}, volume = {7}, number = {2}, pages = {180--195}, abstract = {

A high-order numerical method for three-dimensional hydrodynamics is presented. The present method applies high-order compact schemes in space and a Runge-Kutta scheme in time to solve the Reynolds-averaged Navier-Stokes equations with the $k-ϵ$ turbulence model in an orthogonal curvilinear coordinate system. In addition, a two-dimensional equation is derived from the depth-averaged momentum equations to predict the water level. The proposed method is first validated by its application to simulate flow in a $180^◦$ curved laboratory flume. It is found that the simulated results agree with measurements and are better than those from SIMPLEC algorithm. Then the method is applied to study three-dimensional hydrodynamics in a natural river, and the simulated results are in accordance with measurements.


}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.2014.m605}, url = {http://global-sci.org/intro/article_detail/aamm/12043.html} }
TY - JOUR T1 - A High-Order Numerical Method to Study Three-Dimensional Hydrodynamics in a Natural River AU - Shen , Luyu AU - Lu , Changgen AU - Wu , Weiguo AU - Xue , Shifeng JO - Advances in Applied Mathematics and Mechanics VL - 2 SP - 180 EP - 195 PY - 2018 DA - 2018/05 SN - 7 DO - http://doi.org/10.4208/aamm.2014.m605 UR - https://global-sci.org/intro/article_detail/aamm/12043.html KW - AB -

A high-order numerical method for three-dimensional hydrodynamics is presented. The present method applies high-order compact schemes in space and a Runge-Kutta scheme in time to solve the Reynolds-averaged Navier-Stokes equations with the $k-ϵ$ turbulence model in an orthogonal curvilinear coordinate system. In addition, a two-dimensional equation is derived from the depth-averaged momentum equations to predict the water level. The proposed method is first validated by its application to simulate flow in a $180^◦$ curved laboratory flume. It is found that the simulated results agree with measurements and are better than those from SIMPLEC algorithm. Then the method is applied to study three-dimensional hydrodynamics in a natural river, and the simulated results are in accordance with measurements.


Luyu Shen, Changgen Lu, Weiguo Wu & Shifeng Xue. (1970). A High-Order Numerical Method to Study Three-Dimensional Hydrodynamics in a Natural River. Advances in Applied Mathematics and Mechanics. 7 (2). 180-195. doi:10.4208/aamm.2014.m605
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