Smoothed particle hydrodynamics (SPH) investigation of two-dimensional dam break flows

Taibi S., KorichI K., Hazzab A., Rahou I.

Rahou I., Korichi K.

Abstract This work presents a comparison of two-dimensional numerical solutions of unsteady free surface flow. This is a simulation of the dam-break wave with different configurations using based-mesh finite volume method and meshless smoothed particle hydrodynamics (SPH). Two well-known approaches, widely used in the computational fluid dynamics (CFD). These techniques have proven their robustness in the numerical treatment of such conservation laws. The main goal is to check the ability of the SPH method and the first order finite volume HLLC solver to reproduce the numerical solutions of the 2D shallow water equations. Based on many benchmark tests, one investigates the effect of the topographic variation along the x and y directions on behavior of the numerical solutions namely at the wet-dry front. The comparison between the simulated results, the analytical solutions and the experimental measurements shows a good correlation, although the finite volume approach remains more advantageous in terms of accuracy and the CPU time.

Chang K., Chang T., Garcia M.H.

A well-balanced and positivity-preserving meshless method based on smoothed particle hydrodynamics (SPH) is developed to simulate one-dimensional (1D) and two-dimensional (2D) shallow water (SW) fl...

Khoshkonesh A., Nsom B., Bahmanpouri F., Dehrashid F.A., Adeli A.

This paper aims to evaluate the effects of the opening width of a dam site on the evolution of partial dam-break waves over a fixed dry bed. The volume of fluid (VOF) method was used to scrutinize the propagation of the dam-break free surface. The model was validated using experimental data provided in the literature. At the same time, a sensitivity analysis was conducted on the size of the mesh cells and the turbulence model. However, the large eddy simulation (LES) method showed the highest accuracy among all the models. The results affirmed the crucial role of the opening width of the dam site in the flow characteristics. In this direction, diminishing the opening width results in a reduction of the wave-front travel distance, free surface gradient within the reservoir, outflow discharge values, damping the outflow hydrographs and decreasing the Froude number values at the dam site. Conversely, this leads to an increase in the air bubbles entrained within the wave and results in energy dissipation across the downstream channel.

Wu Y., Tian L., Rubinato M., Gu S., Yu T., Xu Z., Cao P., Wang X., Zhao Q.

Due to its Lagrangian nature, Smoothed Particle Hydrodynamics (SPH) has been used to solve a variety of fluid-dynamic processes with highly nonlinear deformation such as debris flows, wave breaking and impact, multi-phase mixing processes, jet impact, flooding and tsunami inundation, and fluid–structure interactions. In this study, the SPH method is applied to solve the two-dimensional Shallow Water Equations (SWEs), and the solution proposed was validated against two open-source case studies of a 2-D dry-bed dam break with particle splitting and a 2-D dam break with a rectangular obstacle downstream. In addition to the improvement and optimization of the existing algorithm, the CPU-OpenMP parallel computing was also implemented, and it was proven that the CPU-OpenMP parallel computing enhanced the performance for solving the SPH-SWE model, after testing it against three large sets of particles involved in the computational process. The free surface and velocities of the experimental flows were simulated accurately by the numerical model proposed, showing the ability of the SPH model to predict the behavior of debris flows induced by dam-breaks. This validation of the model is crucial to confirm its use in predicting landslides’ behavior in field case studies so that it will be possible to reduce the damage that they cause. All the changes made in the SPH-SWEs method are made open-source in this paper so that more researchers can benefit from the results of this research and understand the characteristics and advantages of the solution proposed.

Monteiro L.R., Lucchese L.V., C. Schettini E.B.

Shallow water models are commonly used to simulate dam-break flow; however, shallow water equations usually assume a hydrostatic pressure assumption that can limit model applications. Dam-break flo...

Chang K., Sheu T.W., Chang T.

In this study, a one- and two-dimensional (1D–2D) coupled model is developed to solve the shallow water equations (SWEs). The solutions are obtained using a Lagrangian meshless method called smoothed particle hydrodynamics (SPH) to simulate shallow water flows in converging, diverging and curved channels. A buffer zone is introduced to exchange information between the 1D and 2D SPH-SWE models. Interpolated water discharge values and water surface levels at the internal boundaries are prescribed as the inflow/outflow boundary conditions in the two SPH-SWE models. In addition, instead of using the SPH summation operator, we directly solve the continuity equation by introducing a diffusive term to suppress oscillations in the predicted water depth. The performance of the two approaches in calculating the water depth is comprehensively compared through a case study of a straight channel. Additionally, three benchmark cases involving converging, diverging and curved channels are adopted to demonstrate the ability of the proposed 1D and 2D coupled SPH-SWE model through comparisons with measured data and predicted mesh-based numerical results. The proposed model provides satisfactory accuracy and guaranteed convergence.

Mokos A., Rogers B.D., Stansby P.K.

Mao J., Zhao L., Bai X., Guo B., Liu Z., Li T.

A well-balanced explicit/semi-implicit finite element scheme is proposed for the simulation of dam break flows over complex domains involving wetting and drying. The numerical model is based on the nonlinear shallow water equations in the hyperbolic conservation form. The governing equations are discretized by a fractional finite element method using a characteristic-Galerkin procedure. Firstly, the intermediate increment of a conserved variable is obtained explicitly neglecting the pressure gradient term. And then, the increment is corrected for the effects of pressure once the pressure increment is obtained from the Poisson equation. In order to maintain the “well-balanced” property, the pressure gradient term and bed slope terms are incorporated into the Poisson equation. Moreover, a local bed slope modification technique is employed in drying-wetting interface treatments. The new model is validated against several benchmark tests and laboratory experimental datas related to dam-break flood wave propagation and promising results are obtained.

Chang T., Chang K., Kao H.

Summary A new approach to model weakly nonhydrostatic shallow water flows in open channels is proposed by using a Lagrangian meshless method, smoothed particle hydrodynamics (SPH). The Lagrangian form of the Boussinesq equations is solved through SPH to merge the local and convective derivatives as the material derivative. In the numerical SPH procedure, the present study uses a predictor–corrector method, in which the pure space derivative terms (the hydrostatic and source terms) are explicitly solved and the mixed space and time derivatives term (the material term of B1 and B2) is computed with an implicit scheme. It is thus a convenient tool in the processes of the space discretization compared to other Eulerian approaches. Four typical benchmark problems in weakly nonhydrostatic shallow water flows, including solitary wave propagation, nonlinear interaction of two solitary waves, dambreak flow propagation, and undular bore development, are selected to employ model validation under the closed and open boundary conditions. Numerical results are compared with the analytical solutions or published laboratory and numerical results. It is found that the proposed approach is capable of resolving weakly nonhydrostatic shallow water flows. Thus, the proposed SPH approach can supplement the lack of the SPH–Boussinesq researches in the literatures, and provide an alternative to model weakly nonhydrostatic shallow water flows in open channels.

Chang T., Chang K.

AbstractIn this study, the authors solve the shallow water equations (SWE) with smoothed particle hydrodynamics (SPH) for one-dimensional (1D) nonrectangular and nonprismatic channel flows with open boundaries. To date, 1D SPH-SWE has been only developed to simulate rectangular prismatic channel flows with closed and open boundaries. However, for practical hydraulic problems, channel cross sections are not always rectangular and prismatic. A general approach is proposed in this study to extend the engineering application range of 1D SPH-SWE to nonrectangular and nonprismatic channels with open boundaries by introducing the wetted cross-sectional area and the water discharge in SWE and combining the method of specified time interval with the inflow/outflow algorithm. Three benchmark study cases, aiming at testing various steady flow regimes in nonrectangular and nonprismatic channels, are adopted to validate the newly proposed approach. Through the investigation of the convergence analysis and numerical ac...

LaRocque L.A., Imran J., Chaudhry M.H.

AbstractThis paper presents measurements of velocity profiles obtained from idealized dam-break experiments and results from numerical simulations of these experiments. Dam-break flows were generated in the laboratory by suddenly lifting a gate inside a flume for three different upstream heads with a dry-bed downstream condition. Ultrasonic Doppler velocity profilers were used for recording transient velocity profiles at eight different locations upstream and downstream of the removed gate. These experiments provided data on the spatio-temporal evolution of the flow field in an unsteady flow of relatively short duration. The two-dimensional experiments were simulated using a computational fluid dynamics solver. The following observations are made: (1) turbulence modeling does not affect the velocity profile in the upstream reservoir, but has significant influence on the prediction of downstream velocity; (2) the velocity magnitude at a specific location changes with time, but the shape of the velocity pro...

Chang T., Chang K., Kao H., Chang Y.

This study develops a new concentration estimation method for Lagrangian modeling of airborne particulate matter (PM) in indoor environment. This new method, based on the cubic spline kernel function with the smoothing length and solid building boundary treatment, is considered herein to study the accuracy and efficiency of indoor airborne PM concentration calculation. The commonly used sampling volume method is also adopted for numerical performance test. Reliable measured PM concentration profiles in indoor chambers are used to verify the accuracy and efficiency of the above methods. A comparison of the relative merits and shortcomings of these two methods is emphasized. The results show that the sampling volume method is simple and easy to formulate in indoor environment. However, it produces sensitive and scattered concentration profiles, especially in recirculation zones, if the released particle number is not large enough. This problem can only be solved by using a sufficient number of particles, which should be determined by the sensitivity analysis. The kernel method can provide accurate and smooth profiles even though the released particle number is one order less than the sampling volume method. Under the same PM concentration estimation accuracy, the kernel method is much more efficient compared to the sampling volume method. ► The kernel method is compared with the sampling volume method for estimating PM concentration. ► The kernel method can provide accurate results even though the lower particle number is released. ► Under the same PM concentration estimation accuracy, the kernel method is much more efficient.

Kao H., Chang T.

Summary Smoothed particle hydrodynamics (SPH) is used to solve the two-dimensional shallow water equations (2D-SWEs) for modeling dambreak-induced flood and inundation. The Lagrangian concept of cylindrical water particles (CWPs) is adopted to generate horizontal flows in rivers and floodplains. Parameter sensitivity analysis and model validation are described to demonstrate the benefits and limits of the 2D-SPH–SWE modeling. Particular attention is devoted to the numerical performance of dealing with free-surface discontinuities, different upstream/downstream boundary conditions, wetting–drying moving interfaces, river–floodplain roughness sensitivity and complex topography variations. The simulated results indicate that many complicated flow phenomena occurred in dam break flows such as transcritical mixed flows, shock front propagation, overtopping flows, partial reflections, hydraulic jumps, hydraulic drops and multiple wave interaction, can be faithfully simulated. Thus, the proposed SPH approach has proved its robustness and reliability for 2D flood and inundation simulations, and can provide an alternative to investigate practical hydraulic engineering problems.

Vacondio R., Rogers B.D., Stansby P.K., Mignosa P.

AbstractA smoothed particle hydrodynamics (SPH) numerical model for shallow water equations (SWEs) is presented for simulating flood inundation owing to rapidly varying flow, such as dam breaks, tsunamis, and levee breaches. Important theoretical and numerical developments have recently been made, and the model in this paper incorporates these developments and implements open boundary conditions, resulting in a general, accurate computational tool suitable for practical application. The method is attractive for flood simulation over large domains in which the extent of inundation is unknown because computation is carried out only in wet areas and is dynamically adaptive. The open boundary algorithm is very general, on the basis of a simplified version of the characteristics method, handling both supercritical and subcritical inflow and outflow. This is tested against reference solutions for flows over a hump involving shocks. The model is then applied to two very different flood inundations resulting from...