An algorithmic implementation of physical reflective boundary conditions in particle methods: Collision detection and response

Abstract

The aim of this paper is to present a computational algorithmic implementation of physical reflective boundary conditions and applications, for use in particle methods. It is motivated by the lack of a straightforward study in the literature dedicated to the presentation of this reflective boundary condition, based on Newton’s restitution law and the foundations of analytic geometry. Particular attention is given here to the procedures of collision detection and response. The importance of the consistency of input data and an appropriate temporal integration technique for use in the particle method is also discussed. Validation tests are performed, with the results of the algorithm verified using analytical results. Numerical simulations of static and dynamic problems are carried out. The analysis of the numerical results shows that the physical reflective boundary conditions are consistent and that the algorithm has been properly implemented.

Reflective boundary conditions coupled with the SPH method for the three-dimensional simulation of fluid-structure interaction with solid boundaries

“…Navier-Stokes equations, presented in the previous section, can be written using the SPH formulation -Eqs. ( 3) and (4). (4) where 𝑊 is the smoothing function or kernel; 𝑿 is the spatial position occupied by the particle; ℎ is the smoothing length; 𝑛 is the number of neighbouring particles inside the domain of influence; 𝑎 and 𝑏 are subscripts that refer to the reference and neighbour particle, respectively.…”

“…This paper incorporates the theory and literature simulation results of research carried out by this author in recent years (2017-2022). First, the computer code implemented with the SPH method coupled with RBC was employed to simulate two-dimensional dam-breaking fluid flow [30,4,5]. This is usually one of the first FSI problems simulated by a numerical code utilising particle modelling.…”

“…It consists of a wave created after opening a gate, colliding against the reservoir walls. A two-dimensional (2D) hydrostatic problem -an incompressible and isothermal still fluid inside an immobile reservoir -was also simulated and validated [4,5].…”

Smoothed Particle Hydrodynamics Modeling with Advanced Boundary Conditions for Two-Dimensional Dam-Break Floods

“…Shortly after collision detection, the particles are reflected; the collision detection and response procedures are then repeated until the particles return to the flow region. More specifically, the resolution of the momentum conservation equation provides the acceleration of the particles at each time step [46,47]. Subsequently, when coupled with an integration method (Euler's method), one can obtain accurate estimates of the particles' final positions and velocities.…”

“…Subsequently, when coupled with an integration method (Euler's method), one can obtain accurate estimates of the particles' final positions and velocities. The convergence and precision of the particles' final positions depend on the quality of the reflections evaluated by the algorithm [47]. Other boundary treatment techniques currently being developed include: a semi-analytical method with the estimation of the contact forces in rigid boundaries [48], an enhanced form of the latter with wall-corrected gradients to be used under general 2D [49,50] and 3D [51] boundary conditions, a boundary integral approach proposed by the authors of [52], and a new SPH model presented by the authors of [53] for viscous and non-viscous flows with 3D complex boundaries.…”