# A Mesh-Free Particle Method for Simulation of Mobile-Bed Behavior Induced by Dam Break
## 1 Introduction  
Due to the highly concentrated energy, the flows induced by a dam break are very violent and include a large deformation of free surface and non-linearity. When it propagates along the river and channel, a severe flood and structural damage can follow. In this regard, the dam break problem has been theoretically, experimentally, and numerically studied by [PERSON] et al. and [PERSON] et al. [1; 2]. Furthermore, [PERSON] et al. investigated the soil bed behavior due to the flows induced by the dam break [3; 4; 5]. In the experimental and theoretical method, the dynamics of strong turbulence at the free surface and wave profiles were investigated by [PERSON] et al. [6; 7]. [PERSON] et al. outlined sediment transport due to dam break swash uprush numerically [5]. In Reference [5], the collision of the collapsed water column to the soil bed in the inclined tank was investigated both experimentally and numerically by [PERSON] et al. Despite many efforts to analyze it, its complication and non-linearity cannot be solved easily. The complexity increases dramatically especially when the flows collide with the structures or movable soil bed. Therefore, accurate analysis is very important for estimating consequences and preparing a counter measure. Computational fluid dynamics (CFD) is an effective method for simulating the violent flows with the large deformation of a free surface including the dam break problem. Conventionally, CFD methods are based on the Eulerian approach, which uses mesh/grid to calculate flows and flux. In this method, flux across a fixed grid is used to calculate velocity and pressure of flows. However, several problems still exist in relation to expecting large deformation of the free surface. In this regard, the methodof volume of fluid (VOF) and the level set are implemented into the programme [8]. Despite using these special treatments, it has been difficult to simulate the complicated phenomena due to large deformation, fragmentation, and coalescence in order to solve those problems [9]. Another problem of the conventional grid-based CFD method is a numerical diffusion induced by an advection term of the governing equation [10; 11]. [PERSON] et al. detailed heterogeneous erodible beds under transient flows by using the Hirano model and the Exner equation [12; 13]. In References [12; 13], two-dimensional (2D) morphodynamics was solved by a set of two equations under the assumption of influenced thickness and roughness of the bed due to time-varying surface textures by [PERSON] et al. Those two investigations contribute and extend the possibility of having heterogeneous beds. The particle method has been used to investigate solid object transportation under large flows. The large floating body transport in the flash floods problem was investigated by [PERSON] et al. [14]. [PERSON] et al. applied the three-dimensional smoothed particle hydrodynamics (SPH) method on three-dimensional (3D) solid body transport in free surface flows [15]. In their work, the weakly compressible-SPH model for the main flow implemented a free-slip boundary condition on the solid body. The moving particle semi-implicit (MPS) method was also employed to simulate solid object movement under large waves. [PERSON] and [PERSON] investigated a mobile-sea bed problem by using the MPS method, and introducing the particle interaction model between two different types of fluids [16]. The particle method is based on the fully Lagrangian approach CFD method. In the particle method, all of the material, including the fluid, is comprised of particles. Each particle travels through the computational domain carrying physical phenomena including position, velocity, acceleration, and pressure. In this regard, the non-linearity, including the large disturbance of the free surface, sharp coalescent, and fragmentation, can be handled straightforwardly by tracking each particle. Another advantage of the particle method is the advection term in the Navier-Stokes equation, which is one of the governing equations that cannot be used.