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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

DOI: 10.4208/aamm.2014.m605

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 = {Shen , LuyuLu , ChanggenWu , Weiguo and Xue , Shifeng}, 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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