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Comments on the paper “Mathematical model for the free surface flow under a sluice gate” by Titus Petrila, published in Applied Mathematics and Computation 125 (2002) 49–58
Applied Mathematics and Computation 148 (2004) 807–808 www.elsevier.com/locate/amc
Comments on the paper ‘‘Mathematical model for the free surface flow under a sluice gate’’ by Titus Petrila, published in Applied Mathematics and Computation 125 (2002) 49–58 Ioan Pop Faculty of Mathematics, University of Cluj, R-3400 Cluj CP 253, Romania
I was amused reading this purely formal and highly artificial paper since all the analysis is merely speculative than logical. For example, the statement made by the author that the conformal mapping 2 f ¼ log p
1þt 1t
where t ¼ reir , r ¼ 1 and 0 6 r 6 p, transforms the flow field shown in Fig. 1 onto the upper half of the unit disk centred at the origin of the complex t-plane is not really exact. This conformal mapping contains singularities at r ¼ 0 and p, which drastically changes the physics of the problem. It should also be mentioned that there are many inconsistencies into the paper. For example, the kinematics (slip) condition on the line BC is given as u sin c þ v cos c ¼ 0 on page 52 and, respectively, u cos c þ v sin c ¼ 0 on page 55, so that the relation dv=dr ¼ ðdu=drÞtgc is wrong. Further, we mention that the problem is faced only analytically and is not related to any numerical results to be compared with those of Vanden–Broeck et al. [4–6]. Therefore, the authorÕs claim that his analytical solution solves the problem under consideration is not true. In fact, the correct solution of this problem is only that presented numerically in the papers [4–6].
E-mail address: [email protected] (I. Pop). 0096-3003/$ - see front matter Ó 2003 Elsevier Inc. All rights reserved. doi:10.1016/S0096-3003(02)00938-4
808
I. Pop / Appl. Math. Comput. 148 (2004) 807–808
In summary, I have a strong feeling that this paper is completely wrong as is that quoted in Ref. [12]. The readers of Applied Mathematics and Computation do not gain something reading this paper, which is of doubtful validity.
Comments on the paper ‘‘Mathematical model for the free surface flow under a sluice gate’’ by Titus Petrila, published in Applied Mathematics and Computation 125 (2002) 49–58 Ioan Pop Faculty of Mathematics, University of Cluj, R-3400 Cluj CP 253, Romania
I was amused reading this purely formal and highly artificial paper since all the analysis is merely speculative than logical. For example, the statement made by the author that the conformal mapping 2 f ¼ log p
1þt 1t
where t ¼ reir , r ¼ 1 and 0 6 r 6 p, transforms the flow field shown in Fig. 1 onto the upper half of the unit disk centred at the origin of the complex t-plane is not really exact. This conformal mapping contains singularities at r ¼ 0 and p, which drastically changes the physics of the problem. It should also be mentioned that there are many inconsistencies into the paper. For example, the kinematics (slip) condition on the line BC is given as u sin c þ v cos c ¼ 0 on page 52 and, respectively, u cos c þ v sin c ¼ 0 on page 55, so that the relation dv=dr ¼ ðdu=drÞtgc is wrong. Further, we mention that the problem is faced only analytically and is not related to any numerical results to be compared with those of Vanden–Broeck et al. [4–6]. Therefore, the authorÕs claim that his analytical solution solves the problem under consideration is not true. In fact, the correct solution of this problem is only that presented numerically in the papers [4–6].
E-mail address: [email protected] (I. Pop). 0096-3003/$ - see front matter Ó 2003 Elsevier Inc. All rights reserved. doi:10.1016/S0096-3003(02)00938-4
808
I. Pop / Appl. Math. Comput. 148 (2004) 807–808
In summary, I have a strong feeling that this paper is completely wrong as is that quoted in Ref. [12]. The readers of Applied Mathematics and Computation do not gain something reading this paper, which is of doubtful validity.