Numerical modeling of flood waves in a bumpy channel with the different boundary conditions

Transcription

1 Numerical modeling of flood waves in a bumpy channel with the different boundary conditions Sajedeh Farmani 1*, Gholamabbas Barani 2, Mahnaz Ghaeini-Hessaroeyeh 3, Rasoul Memarzadeh 4 1 Ph.D Candidate, Department of Civil Engineering, Faculty of Engineering, Shahid Bahonar University of Kerman, PO Box , Kerman, Iran sajedeh.farmani@eng.uk.ac.ir Telephone number: Mobile number: Professor, Department of Civil Engineering, Faculty of Engineering, Shahid Bahonar University of Kerman, PO Box , Kerman, Iran. gab@uk.ac.ir Telephone number: Mobile number: Assistant Professor, Department of Civil Engineering, Faculty of Engineering, Shahid Bahonar University of Kerman, PO Box , Kerman, Iran. mghaeini@uk.ac.ir 4 Ph.D of civil (hydraulic structurs) engineering, Department of Civil Engineering, Faculty of Engineering, Shahid Bahonar University of Kerman, PO Box , Kerman, Iran. Telephone number: Mobile number: rasoul.memarzadeh@eng.uk.ac.ir Mobile number:

2 Abstract In this paper, the Incompressible Smoothed Particle Hydrodynamics (ISPH) method is presented to simulate flood waves in uneven beds. The SPH method is a mesh free particle modeling approach that is capable of tracking the large deformation of free surfaces in an easy and accurate manner. Wave breaking is one of the phenomena that its free surface is complicated. Therefore, ISPH method is robust tool for the modeling of this kind of free surface. The basic equations are the incompressible mass conservation and Navier Stokes equations that are solved using a two-step fractional method. In the first step, these equations are solved to compute velocity components by omitting the pressure term and in the absence of incompressible condition. In the second step, the continuity constraint is satisfied and the Poisson equation is solved to calculate pressure terms. In the present model, a new technique is applied to allocate density of the particles for the calculations. By employing this technique, ISPH method is stabled. The validation by comparison with laboratory data is conducted for bumpy channel with various boundary conditions. The numerical results showed good agreement with available experimental data. Also relative error is calculated for two numerical cases. Key words: Flood waves, ISPH method, Wave breaking, Uneven bed, Fractional method 1. Introduction Flood waves is a complex phenomenon that occurs in free surface flows with large deformation. Dam break wave is one of this flow that can be caused losses and damages. Therefore prediction of the water level position, velocity and pressure are essential. These problems are difficult to simulate due to the existence of the arbitrarily moving surface boundary conditions and also because of the complex governing Navier Stokes Equations (NSEs) [1]. Also, the dam break problem has been the subject of many analytical, experimental, and numerical studies for hydraulics scientists and engineers [2,3,4].The marker and cell [5] and Volume Of Fluid (VOF), [6] methods are the most common methods for simulating such flows, in which the Navier Stokes equations are solved on a fixed Eulerian grid [7]. In MAC method marker particles were used to define the free surface while in VOF method the governing equations are solved for the volume fraction of the fluid. However, in spite of successful use of both methods for treating free surface flows, numerical diffusion due to solving NSEs on a fixed Eulerian grid arose, especially when the deformation of free surface is very large [8]. In the general area of computational mechanics there is a growing interest in developing so-called meshless/ meshfree methods 2

3 or particle methods as alternatives to traditional grid-based methods such as finite difference methods and finite element methods [9]. One of the oldest mesh-less methods is the Smoothed Particle Hydrodynamics (SPH) method. Smoothed particle method is originally used for astronomic problems. Recently, this method has been well studied and applied in computational fluid dynamics, specially for flows with complex free surface [10]. Furthermore, SPH method was used successfully to model the fixed-bed dam break flow on a dry-bed and wet-bed downstream channel [11, 12]. Ozbulut et al. [13] carried out a numerical investigation into the correction algorithms for SPH method in modelling violent free surface flows. SPH simulations of the incompressible flows can be carried out by two approaches: 1) approximately simulating incompressible flows with a small compressibility, or Weakly Compressible SPH (WCSPH); 2) simulating flows by enforcing incompressibility, or Incompressible SPH (ISPH). In WCSPH method, the flow is considered as slightly compressible, with a state equation for the pressure calculation [14, 15]. In ISPH method the pressure-velocity coupling is generally solved by the projection method [16, 17, 18, 19]. In this field, Xenakis et al. [20] improved the pressure predictions using an incompressible SPH scheme for free surface Newtonian flows. Nomeritae et al. [21] presented an explicit incompressible SPH algorithm for free surface flow and then compared this algorithm with weakly compressible scheme. This paper presents an incompressible 2D ISPH model to simulate flood waves in uneven bed and validated in Sections 5, for a rough bumpy channel with various boundary conditions. Furthermore the relative error are calculated in the different section. 2. Governing equations The Navier Stokes equations (mass and momentum conservation equations) are written in 2D Lagrangian form as [3]: 1 D. u 0 (1) Dt 3

4 Du Dt 1 2 p b u f (2) where is the flow density, u is the flow velocity, p is the pressure, is dynamic viscosity, fb represents the body force and t is time. Equation (1) is in the form of a compressible flow. Incompressibility is enforced in a correction step of the time integration by setting Dρ Dt = 0 at each particle. The motion of each particle is calculated by Dr/ Dt = u, with r being the position vector. These equations were solved by SPH method. 3. Numerical methodology 3.1. ISPH formulations In the SPH method the fluid domain is represented by nodal points that are scattered in space with no definable grid structure and move with the fluid. Each of these nodal points has information, such as density, pressure, velocity components, etc. [22]. The SPH formulation is obtained as a result of interpolation between a set of disordered points known as particles. The interpolation is based on the theory of integral interpolants that uses a kernel function to approximate delta function. The kernel approximation of f is written in the form [23]: f ( r) f ( r) W( r r, h) dr (3) 0 In the particle approximation, for any function of field variable: m n j f ( ri ) f ( r ) W ( r r, h) (4) j 1 j i j j that, is the support domain, m j and are the mass and density of particle j, mj j is the volume j element associated with particle j, W is interpolation kernel function (in this paper kernel based on the spline function is used [23]), r is the position vector, h is the smoothing distance which determines width of kernel and ultimately the resolution of the method and in this paper h 1.2 dr are used, where dr is 4

5 the initial particle spacing, and n is the total number of particles within the smoothing that affects particle i. For example density of a particle in the SPH approximation represented as: n m W ( r r, h) (5) i j i j j 1 The formulation of the gradient term has different forms depending on the derivation used [23]. The gradient of the pressure is expressed as: 1 P P ( ) ( ) j i Pi m j W 2 2 ij i j j i (6) where, P is pressure of the particles. Similarly, the divergence of a vector u at particle i can be expressed by: u u. u m ( ). W i j i i j 2 2 i ij j i j (7) The Laplacian for the pressure and viscosity term is formulated as the hybrid of a standard SPH first derivative coupled with a finite difference approximation for the first derivative [4]. Furthermore, it has been found that the resulting second derivative of the kernel is very sensitive to particle disorder and will easily lead to pressure instability and decoupling in the computation due to the co-location of the velocity and pressure [8]. These are represented by: 1 8 P ij rij. iwij.( P) i m 2 ρ (ρ ρ ) η j 2 2 j i j rij (8) 4 m ( ) r. W 2 j i j ij i ij ( u ) i (u ) i- u j j ( i j ) ( rij ) (9) in which, Pij Pi Pj, ij i j r r r, is the viscosity coefficient and is a small number introduced to keep the denominator no-zero during computational and usually equal to 0.1h. After employing the 5

6 SPH formulation equation (9) for the Laplacian of pressure, the corresponding coefficient matrix of linear equations is symmetric and positive definite and can be efficiently solved by available solvers Limitation of time step In the simulation of water flows, in which the fluid viscosity is not a control factor, the stability of the ISPH computation requires the following Courant condition to be observed: t 0.1 x (10) v max where v max denotes the maximum particle velocity in the computational domain. The factor 0.1 ensures that the particle moves only a small fraction of the particle spacing per time step [24] Boundary conditions Free surface boundary The ISPH model uses the particle density to judge the free surface and a zero pressure is given to these particles. The criterion is that there is no fluid particle existing in the outer region of the free surface, so the particle density on the surface should drop significantly [8]. Therefore a particle which satisfies the following equation was considered to be on the free surface: ( ) ( ) (11) * i 0 i In this equation β is the free surface parameter and [25]. In this paper 0.94 is used. The equation (11) is applied to the free surface particles, in order to move correctly, avoid instability in the computations and control over their incompressibility condition [1] Solid wall boundaries Solid walls are simulated by one line of particles. In order to satisfy the non-slip boundary condition, the velocities of wall particles are set to zero. For the balance of the pressure of inner fluid particles and prevent them from penetrating the solid walls, the pressure Poisson equation is solved for these wall particles and the Neumann boundary condition is imposed. Also, two lines of dummy particles places 6

7 outside of wall boundaries and their pressure is set to that of a wall particle in the normal direction of the solid walls. By imposing these conditions, the density of particles is computed accurately and wall particles are not considered as free surface particles [8]. 4. Solution algorithm At first, the initial conditions such as problem geometry, smoothing distance, number of particles, mass, dynamic viscosity, initial coordinate and their velocity, are defined. Then two steps fractional algorithm are applied. In the first step, the Navier Stokes equations are solved to compute velocity components without the pressure term and in the absence of incompressible condition. In the second step, the continuity constraint is satisfied and the resulting Poisson equation is solved to calculate pressure terms [8]. This algorithm can be summarized in five stages: - Calculate the density of the particles using the equation [8]: m W( r r, h) 0 i j j i j (12) - The prediction step: Compute temporary particle positions and velocities by considering the gravity and viscosity term in equation (2) [8]: 2 u * ( g u ) t (13) u u u (14) * t * * r rt u * t (15) where u t and r t are the particle velocity and position at time t; u * and * r are the temporary particle velocity and position, respectively and u * is changed in the particle velocity during the prediction step. In this step, due to omitting the pressure term, the fluid density is changed, and is computed again by equation 16. Therefore incompressibility is not still satisfied [8]. 7

8 m W( r r, h) * * * i j i j j (16) - The correction step; in this step the pressure term, is computed from Poisson equation (equation 19) by considering the continuity constraint and enforcing incompressibility with combining equations 17 and 18, [8]: *.( u **) 0 (17) t 1 u P t (18) ** t 1 * 1.( P ) ρ 0 * t 1 2 * 0 t (19) The Poisson equation produces a system of linear equation that is solved by iterative solvers. - New particle velocities are obtained from equations (19) and (20), [8]. u =u Δu (20) t 1 t ** -The new position of particles is computed by the equation (21), [8]. r r u u 2 t 1 t t 1 t t (21) 5. Numerical validations In this section, the numerical accuracy and applicability of the proposed ISPH method are examined by the laboratory measurements of dam-break flows in the bumpy channel Dry bed with open end Problem geometry and solution domain 8

9 In this case, the experimental data of Ozmen-Cagatay et al. [26] are used. Dimensions of the channel and reservoir are displayed in figure 1. All of the bed is dry before and after the obstacle and there is an open end boundary condition Qualitative description of the flow After lifting the gate, the water wave propagates over the bed. After about t= 0.9s, the flow water hits the obstacle. At t=1.36s, amount of water passes the bump while at t=2.8s, the wave reflection of the bump is clearly observed. The water flow and propagation of waves are shown in figure 2 for t=0.22s, t=0.5s, t=0.9s, t=1.36s, t=2.8s, t=3.3s, t=3.68s, t=4.74s, t=5.72s. The good agreement exists between the present model results and the experimental data Comparison of free surface profile with experimental data The free surface profiles are shown in figure 3 and the results of the present model is compared with experimental data of Ozmen-cagatay et al. [26]. Be noted that the space and the level of water are dimensionless and the time is multiplied by 0.5 ( g / h o ) and then the dimensionless time 0.5 T t ( g / ho ) is obtained ( g and ho are gravity acceleration and initial depth of water respectively). According to the figure 3, at T=15.16 and T=17.54 and on the top of the obstacle, the estimate of water level of numerical model is slightly higher than the experimental data of Ozmen-Cagatay et al. [26], but in both, the maximum of the water depth happened on the peak of the bump (bump is triangular obstacle that shown in figure 3). At T=20.67, from the first of the bed up to the end of the bump, the numerical model slightly overestimates the water level. From T=20.67 up to T=35.83, when the flow wave reaches the bump, a part of water is reflected and another part passes the bump. At T=23.05 before the obstacle, the free surface profile of the present model is higher than in the experimental data. At T=29.69 and T=35.83, the water level at the upstream of the bump is changeless in the numerical model. At the time progress (T>35.83), the water level is maximum at the top of the bump. At T=41.84 and T=49.99, the results of the present model are in good agreement with the experimental data. 9

10 Calculation of relative error By comparing the results of the numerical model with experimental data, relative error is calculated as follows: X Computational X Experimental Error(%) 100 (26) X Experimental The resulting is shown in table Water level variation over time The location of the stations P1, P2, P3, P4, P5 and P6 are shown in figure 4. Dimensionless level of water over time is compared with experimental data at these points. This comparison is displayed in figure 5. The plots are depicted for 9.5 second. After sudden removal the gate, a decline and rise in water level occur for P1 and p2 respectively up to T=5. From T=5 to T=40, the water level changes a little at these points. After the passing and reflection of water wave of the bump (T=40), the water level decline gradually at P1 and P2. When the wave front reaches the P3, the water level increases suddenly. The duration of the water level being constant (T=20-29) is shorter for P3 than those for P1 and P2. At P4, P5, P6, the water level grows without being constant. The free surface flow changes a little behind the negative wave. At this time, the flow transmute to the subcritical flow via hydraulic jump and then passes the bump. At this stage, the water levels remain constant in maximum values, because inflow and outflow are in balance. At T>40 the water level declines in downstream while negative wave moves to the upstream. In general, the good agreement exists between the present model results and the experimental data Calculation of relative error As for the section 5.1.6, the relative error is calculated using the equation 26. Therefore the resulting is shown in table Wet bed after obstacle with closed end 10

11 In this case, the experimental data of Soares Frazao et al. [27] are selected for comparison. Initial domain and dimensions are shown in figure 6. There is closed end boundary condition and the bed is dry before the bump and wet after it Qualitative description of the flow The flow is described at t=1.8s, t=3.0s, t=3.7s and t=8.4s and images are shown in figure 7. When the gate is opened, the flows move to the downstream. After the water reaches the obstacle, part of the wave crosses the bump, but another part is reflected and moves to the upstream. After crossing the bump, the flow reaches the pool of water. In this time (t=3.0s), a positive front wave is formed and travels to the upstream. Then this flow moves to the bed and reaches the bump and is reflected again (t=3.7). At t=8.4s the water on the bump is balanced Comparison of the free surface profile with the experimental data In this section, Comparison of the free surface profile with the experimental data are carried out. Then the results are shown in figure 8, at t=1.8s, t=3.0s, t=3.7s and t=8.4s. In these times, the present model reproduces good results Calculation of relative error The calculation of error is the same as sections and that are given in table Rectangular obstacle In this section, the liquid behavior, when it hits to the rectangular obstacle, is investigated and compared with the experimental data of Koshizuka et al. [28]. The initial geometry of this case is provided in figure 9. This figure illustrates the experimental data and the numerical results at t=0.1, 0.2, 0.3, 0.5 s. at t=0.5s, the results of the numerical model is slightly different with the experimental data. Because of air faze is neglected in the numerical model. The good agreement exist between the experimental data and the numerical results. 6. Discussions 11

12 In the previous sections, the flood waves in the channel with the different boundary conditions were investigated. Case one was a channel with dry bed and open end. Dam break problem was studied in this channel. Then the free surface profile was compared with the experimental data of Ozmen-Cagatay et al. [26]. The results of this model was in very good agreement with the experimental data. Also maximum of relative error was calculated for different dimensionless times and shown good accuracy for numerical model. The second case was channel with the closed end that the bed after the obstacle was considered wet. Then dam break waves were investigated for this case. This problem was compared with the experimental data of Soares Frazao et al. [27]. At the end of this part, maximum of relative error was computed for different times. By analysis of the results and maximum of error could be found that the results of the present model had good efficiency for modeling the interference of waves. In the third case, a channel with a rectangular obstacle was considered. For this example, the results of the present model are compared with the experimental data of Kushizuka et al. [21]. For this case, flow of dam break had acceptable accordance in comparison the experimental data. 7. Conclusion In this paper a numerical modelling of flood waves in a bumpy channel with the different boundary conditions is developed. An ISPH Method is presented to simulate flood waves in a bumpy channel with the different boundary conditions. SPH is a Lagrangian particle method which does not require a grid to simulate free surface flows. Wave breaking is one of the phenomena that its free surface is complicated. Therefore particle methods such as ISPH method is robust tool for the modelling of this kind of free surface. The method employs particles to discretize the Navier Stokes equations and the interactions among particles simulate the flows. Thus the advection terms in Navier-Stocks equations are calculated directly which this omit numerical diffusion errors. In the present model, a new technique is applied to allocate density of the particles for the calculations. By employing this technique, ISPH method is stabled. The numerical validation and verification are performed through experimental data to proving capability of the ISPH model to simulate flood waves interaction in uneven beds with various.boundary 12

13 conditions. Also the results shown that the free surface flows in the channels with the different boundary conditions are simulated using ISPH method with high accuracy. In other side, the computed relative error indicates this fact too. References [1] Ataie-Ashtiani, B., Shobeiry, G., Farhadi, L. Modified Incompressible SPH method for simulating free surface problems, Fluid Dynamic Research, 40, PP (2008). [2] Stoker, JJ. Water waves. Pure and applied mathematics 4. Interscience Publishers, New York. (1957) [3] Xia, J., Lin, B., Falconer, RA., Wang, G. Modelling dam-break flows over mobile beds using a 2D coupled approach. Adv Water Resour. 33(2), pp (2010). [4] Shakibaeinia, A., Jin, YC. A mesh-free particle model for simulation of mobile-bed dam break. Adv Water Resour. 34(6), (2011) [5] Harlow, F., Welch, J. Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface, The physics of fluids, 8 (12), PP (1965). [6] Hirt, C.W., Nichols, B.D. Volume of Fluid (VOF) Method for the Dynamics of Free Boundaries, Journal of Computational Physics, 39, PP (1981). [7] Khanpour, M., Zarrati, A.R., Kolahdoozan, M., Numerical simulation of the ow under sluice gates by SPH model Sharif University of Technology, Scientia Iranica,Transactions A: Civil Engineering, 21 (5), pp (2014). [8] Shao, S., E. Lo E. Incompressible SPH method for simulating Newtonian and non-newtonian flows with a free surface, Advances in Water Resources, 26, PP (2003). [9] Fang, J., Parriaux, A., Rentschler, M., Ancey, Ch. Improved SPH method for simulating free surface flows of viscous fluids, Applied Numerical Mathematics, 59, pp. 251_271 (2009). [10] Wang, B.L., Liu, H. Application of SPH method on free surface flows on GPU, Journal of Hydrodynamics, 22(5), PP. 912_914 (2010). [11] Lee, E.S., Xu, C., Moulinec, R., Violeau, D., Laurence, D., Stansby, P. Comparisons of Weakly Compressible and Truly Incompressible Algorithms for the SPH Mesh Free Particle Method, Journal of Computational Physics, 227, PP (2008). [12] Khayyer, A., Gotoh, H. On particle-based simulation of a dam break over a wet bed, J Hydraul 595 Res,48(2), PP (2010). [13] Ozbulut, M. Yildiz, M. Goren, O. A numerical investigation into the correction algorithms for SPH method in modeling violent free surface flows, Journal of Mechanical Sciences, 79, PP (2014). [14] Monaghan, J.J. Simulating free surface flows with SPH, Journal of Computational Physics, 110, PP (1994). [15] Morris, J.P., Fox, P.J., Zhu, Y. Modeling low Reynolds number incompressible flows using SPH, Journal of Computational Physics, 136, PP (1997). [16] Chorin, A.J. Numerical solution of the Navier-Stokes equations, Mathematics of Computation, 22, PP (1968). [17] Cummins, S.J. Rudman, M. An SPH projection method, Journal of Computational Physics, 152, PP (1999). [18] Shao, S., Gotoh, H. Simulating coupled motion of progressive wave and floating curtain wall by SPH-LES model, Coastal Engineering Journal, 46, PP (2004). 13

14 [19] Hu, X.Y., Adams, N.A. An incompressible multi-phase SPH method, Journal of Computational Physics, 227, PP (2007). [20] Xenakis, A.M. Lind, S.J. Stansby, P.K. Rogers, B.D. An incompressible SPH scheme with improved pressure predictions for free-surface generalized Newtonian flows, Journal of Non-Newtonian Fluid Mechanics, 218, PP (2015). [21] Nomeritae, Daly, E. Grimaldi, S. Hong Bui, Ha. Explicite incompressible SPH algorithm for freesurface modeling: A comparison with weakly compressible schemes, Advances in Water Resources, 97, PP (2016). [22] Dalrymple, R.A., Rogers, B.D. Numerical modeling of water waves with the SPH method, Coastal Engineering Journal, 53, PP (2006). [23] Monaghan, J.J. Smoothed particle hydrodynamics, Annu RevAstron Astrophys, 30, PP (1992). [24] Shao, S. Incompressible SPH flow model for wave interactions with porous media, Coastal Engineering Journal, 57, PP (2010). [25] Koshizuka, S., Oka, Y., Moving-Particle Semi-Implicit Method for Fragmentation of Incompressible Fluid, Nuclear Science and Engineering, 123, PP (1996). [26] Ozmen-Cagatay, H., Kocaman, S., Guzel, H. Investigation of dam-break flood waves in a dry channel with a hump, Journal of Hydro-enviroment Research, PP (2014). [27] Soarez Frazao, S., de Bueger, C., Dourson, V., Zech, Y. Dam-break wave over a triangular bottom sill, International conference on fluvial hydraulics, PP (2002). [28] Koshizuka, S., Oka, Y., Tamako, H. A particle method for calculating splashing of incompressible viscous fluid, Int. Conf. Math. Comput. 2, PP (1995). The caption of Figures and tables: Figure 1. The initial geometry of the bumpy channel with dry bed [26] Figure 2. The free surface profiles and pressure field in the present model and the experimental Data of Ozmen- Cagatay et al. [26] at different times for bumpy channel with dry bed. Figure 3. Comparison of the free surface profile between the present model results and the experimental data of Ozmen-Cagatay et al. [26] at different dimensionless time T = (a) 15.16, (b) 17.54, (c) 20.67, (d) 23.05, (e) 29.69, (f) 35.83, (g) 41.84, (h) Figure 4. The location of measurement stations Figure 5. Comparison of the water level between the present model results and the experimental data of Ozmen-Cagatay et al. [26] for time evolution at dimensionless distance X = (a) - 0.6, (b) 0.6, (c) 3, (d) 6, (e) 7, (f) 8. Figure 6..Initial geometry of bumpy channel with wet bed after obstacle [27]. Figure 7. Free surface profile and comparison between the present model results and the experimental data of Soares Frazao et al. [27] at different times for channel with wet bed after the obstacle. 14

15 Figure 8.Comparison of water surface profiles between the present model results and the experimental data of Soares Frazao et al. [27] at different times. Figure 9. Free surface profile and comparison between the present model results and the experimental data of Kushizuka et al. [28] at different times for the channel with rectangular obstacle. Table 1. Maximum of Error calculating at the different dimensionless times shown in figure 3. Table 2. Maximum of Error calculating for points specified in figure 5. Table 3. Maximum of Error calculating at different times shown in figure8. Figure 1 15

16 16

17 Figure 2 17

18 Figure 3 Figure 4 18

19 Figure 5. Figure 6 19

20 Figure 7 20

21 Figure 8 21

22 Figure 9 T 0.5 t g h ) 0 ( / o Table 1 ( h/ h ) Experimental ( h/ h 0) Computational x / h Maximum of Error

23 Table 2. Points ( h/ h 0) Experimental ( h/ h 0) Computational 0.5 T t ( g / ho ) Maximum of Error P1 P2 P3 P4 P5 P Table 3. t(s) Z( m ) Experimental Z( m ) computational X(m) Maximum of Error Sajedeh Farmani received the B.Sc. degree in civil engineering from Bahonar university of Kerman, Iran, in Then, he continued his studies and researches in the fields of Hydraulic engineering. He received the M.Sc. degree in civil (hydraulic) engineering from Bahonar university of Kerman, Iran, in 2014 (with first rank). Now, she is Ph.D. student of civil engineering (hydraulic structures) in Bahonar university of Kerman, Iran. She published more than 6 papers in the international journals and conferences. Her research interests include numerical simulation, dam- break flow, SPH method, numerical modeling of tuned liquid dampers, FEM method in free surface flow and improvement of finite element method in modeling of fluid mechanics. Gholam-Abbas Barani Graduated from UC. Davis at California, USA, 1981 Field of interest is Water resource engineering at present time as civil engineering faculty of Shahid Bahonar University, Kerman since Present situation is professor. Academic activities: a) teaching hydraulics, advanced hydraulics, hydraulic structure and advanced groundwater for BS., MSc and PhD program. b) publishing about 53 papers at international and national journals, presenting and publishing more than 200 paper in national and international conferences. Mahnaz Ghaeini-Hessaroeyeh received her Ph.D. degree in Civil Engineering-Water Engineering of Amirkabir University of Technology in She works as an Assistant Professor in Civil Department of Shahid Bahonar University of Kerman from Jan until now. 23

24 Her research interests include computational fluid dynamics, sediment transport modeling, supercritical flow over hydraulic structures, dam-break flow over movable beds and numerical modeling of ground water flow. She has contributed/presented more than 75 papers in various journals and national and international conferences. Rasoul Memarzadeh received the B.Sc. degree in civil engineering from Vali-e-Asr university of Rafsanjan, Iran, in Then, he continued his studies and researches in the fields of Water and Hydraulic engineering. He received the M.Sc. degree in civil (hydraulic) engineering from the Khaje Nasirodin Toosi university of technology, Tehran, Iran, in 2012 (with first rank), and Ph.D. degree in civil (hydraulic structures) engineering from the Shahid Bahonar University of Kerman, Iran, in 2017 (with first rank), respectively. He published more than 15 papers in the international journals and conferences. His current research interests include hydraulic engineering, fluid mechanics, numerical simulation, computational fluid mechanics (CFD), meshless methods, SPH method, waves and currents, multi-phase flows and sediment transport. 24