SPH study of the evolution of water–water interfaces in dam break flows

The mixing process of upstream and downstream waters in the dam break flow could generate significant ecological impact on the downstream reaches and influence the environmental damages caused by the dam break flood. This is not easily investigated with the analytical and numerical models based on the grid method due to the large deformation of free surface and the water-water interface. In this paper, a weakly compressible Smoothed Particle Hydrodynamics (WCSPH) solver is used to study the advection and mixing process of the water bodies in two-dimensional dam-break flows over a wet bed. The numerical results of the mixing dynamics immediately after the release of the dam water are found to agree satisfactorily with the published experimental and numerical results. Then further investigations are carried out to study the interface development at the later stage of dambreak flows in a long channel. The analyses concentrate on the evolution of the interface at different ratios between the upstream and downstream water depths. The potential capabilities of the mesh-free SPH modelling approach for predicting the detailed development of the water-water interfaces are fully demonstrated.The first author acknowledges the Jafar Studentship during her PhD study at the University of Cambridge. The other authors acknowledge the support of the Major State Basic Research Development Program (973) of China (No. 2013CB036402), Open Fund of the State Key Laboratory of Hydraulics and Mountain River Engineering, Sichuan University (SKHL1404; SKHL1409), Start-up Grant for the Young Teachers of Sichuan University (2014SCU11056) and National Science and Technology Support Plan (2012BAB0513B0).This is the accepted manuscript. The final version is available at http://link.springer.com/article/10.1007%2Fs11069-015-1726-6

A parameter-free total Lagrangian smooth particle hydrodynamics algorithm applied to problems with free surfaces

This paper presents a new Smooth Particle Hydrodynamics computational framework for the solution of inviscid free surface flow problems. The formulation is based on the Total Lagrangian description of a system of first-order conservation laws written in terms of the linear momentum and the Jacobian of the deformation. One of the aims of this paper is to explore the use of Total Lagrangian description in the case of large deformations but without topological changes. In this case, the evaluation of spatial integrals is carried out with respect to the initial undeformed configuration, yielding an extremely efficient formulation where the need for continuous particle neighbouring search is completely circumvented. To guarantee stability from the SPH discretisation point of view, consistently derived Riemann-based numerical dissipation is suitably introduced where global numerical entropy production is demonstrated via a novel technique in terms of the time rate of the Hamiltonian of the system. Since the kernel derivatives presented in this work are fixed in the reference configuration, the non-physical clumping mechanism is completely removed. To fulfil conservation of the global angular momentum, a posteriori (least-squares) projection procedure is introduced. Finally, a wide spectrum of dedicated prototype problems is thoroughly examined. Through these tests, the SPH methodology overcomes by construction a number of persistent numerical drawbacks (e.g. hour-glassing, pressure instability, global conservation and/or completeness issues) commonly found in SPH literature, without resorting to the use of any ad-hoc user-defined artificial stabilisation parameters. Crucially, the overall SPH algorithm yields equal second order of convergence for both velocities and pressure