Erratum for “MacCormack-TVD Finite Difference Solution for Dam Break Hydraulics over Erodible Sediment Beds” by Chaojun Ouyang, Siming He, and Qiang Xu

Ouyang, Chaojun; He, Siming; Xu, Qiang

doi:10.1061/(ASCE)HY.1943-7900.0001348

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Jun 30, 2017

Erratum for “MacCormack-TVD Finite Difference Solution for Dam Break Hydraulics over Erodible Sediment Beds” by Chaojun Ouyang, Siming He, and Qiang Xu

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Authors: Chaojun Ouyang, Siming He, and Qiang XuAuthor Affiliations

Publication: Journal of Hydraulic Engineering

Volume 143, Issue 9

https://doi.org/10.1061/(ASCE)HY.1943-7900.0001348

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Eq. (17) of the original paper requires correction. The minus signs before the third terms in the definitions of

S_{2}

and

T_{3}

,

[(E - D) / (1 - p)] u_{1}

and

[(E - D) / (1 - p)] v_{1}

, should be plus signs. Eq. (17) should therefore be

\frac{\partial X}{\partial t} + \frac{\partial F}{\partial x} + \frac{\partial G}{\partial y} = S + T

(17)

in which

X = {\begin{matrix} h_{1} \\ h_{1} u_{1} \\ h_{1} v_{1} \\ h_{1} c_{1} \\ z_{1 bot} \end{matrix}}; F = {\begin{matrix} h_{1} u_{1} \\ h_{1} u_{1}^{2} + g h_{1}^{2} / 2 \\ h_{1} u_{1} v_{1} \\ h_{1} u_{1} c_{1} \\ 0 \end{matrix}}

G = {\begin{matrix} h_{1} v_{1} \\ h_{1} u_{1} v_{1} \\ h_{1} v_{1}^{2} + g h_{1}^{2} / 2 \\ h_{1} v_{1} c_{1} \\ 0 \end{matrix}}; S = {\begin{matrix} 0 \\ S_{2} \\ 0 \\ 0 \\ 0 \end{matrix}}

T = {\begin{matrix} \frac{E - D}{1 - p} \\ 0 \\ T_{3} \\ E - D \\ - \frac{E - D}{1 - p} \end{matrix}}

and

S_{2} = - g h_{1} \frac{\partial z_{1 bot}}{\partial x} - \frac{(ρ_{s} - ρ_{w}) g h_{1}^{2}}{2 ρ_{1}} \frac{\partial c_{1}}{\partial x} + \frac{E - D}{1 - p} u_{1} - \frac{g n^{2} u_{1} \sqrt{u_{1}^{2} + v_{1}^{2}}}{h_{1}^{1 / 3}}

T_{3} = - g h_{1} \frac{\partial z_{1 bot}}{\partial y} - \frac{(ρ_{s} - ρ_{w}) g h_{1}^{2}}{2 ρ_{1}} \frac{\partial c_{1}}{\partial y} + \frac{E - D}{1 - p} v_{1} - \frac{g n^{2} v_{1} \sqrt{u_{1}^{2} + v_{1}^{2}}}{h_{1}^{1 / 3}}

However, all of the computational cases were calculated correctly from Eqs. (9) and (10), which were correct in the original paper.

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Journal of Hydraulic Engineering

Volume 143 • Issue 9 • September 2017

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Received: Mar 16, 2017

Accepted: Mar 22, 2017

Published online: Jun 30, 2017

Published in print: Sep 1, 2017

Discussion open until: Nov 30, 2017

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Chaojun Ouyang

Associate Researcher, Key Laboratory of Mountain Hazards and Surface Process, Chinese Academy of Sciences, Chengdu 610041, China; Institute of Mountain Hazards and Environment, Chinese Academy of Sciences, Chengdu 610041, China; State Key Laboratory of Geohazard Prevention and Geoenvironment Protection, Chengdu Univ. of Technology, Chengdu 610059, China.

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Siming He

Researcher, Key Laboratory of Mountain Hazards and Surface Process, Chinese Academy of Sciences, Chengdu 610041, China; Institute of Mountain Hazards and Environment, Chinese Academy of Sciences, Chengdu 610041, China (corresponding author). E-mail: [email protected]

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Qiang Xu

State Key Laboratory of Geohazard Prevention and Geoenvironment Protection, Chengdu Univ. of Technology, Chengdu 610059, China.

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Erratum for “MacCormack-TVD Finite Difference Solution for Dam Break Hydraulics over Erodible Sediment Beds” by Chaojun Ouyang, Siming He, and Qiang Xu

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