Numerical Simulation of Two-dimensional Nonlinear Waves on Beaches Using a Smoothed Particle Hydrodynamics Method

The study concerns the application of the smoothed particle hydrodynamics (SPH) method within computational fluid dynamics. In the present study, a tank discharge with a falling head is investigated. Water is modelled as a viscous fluid with weak compressibility. An enhanced treatment of the solid boundaries is used within the two-dimensional SPH scheme. The boundaries are represented by a special set of SPH particles that differ from the ones representing the fluid by being immovable, preventing the fluid from leaving the container. Particles with different colors are used to illustrate the sequence of the empting the tank as well as the velocity vectors to show stream lines. A code is developed using C++ to solve all equations explicitly by use of a Verlet algorithm. Results are compared to an analytical solution, and a good agreement is achieved.

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Mathematical modeling of the electron-beam wire deposition additive manufacturing by the smoothed particle hydrodynamics method

Mechanics of Advanced Materials and Modern Processes ◽

10.1186/s40759-019-0044-1 ◽

2019 ◽

Vol 5 (1) ◽

Author(s):

Dmitriy Nikolayevich Trushnikov ◽

Elena Georgieva Koleva ◽

Roman Pozolovich Davlyatshin ◽

Roman Mikhailovich Gerasimov ◽

Yuriy Vitalievich Bayandin

Keyword(s):

Numerical Simulation ◽

Mass Transfer ◽

Electron Beam ◽

Additive Manufacturing ◽

Heat And Mass Transfer ◽

Smoothed Particle Hydrodynamics ◽

Lagrangian Description ◽

Particle Hydrodynamics ◽

Smoothed Particle ◽

Smoothed Particle Hydrodynamics Method

Abstract Background The actual problem for calculating a shape of free surface of the melt when analyzing the processes of wire-based electron-beam surfacing on the substrate, being introduced into additive manufacturing, is the development of adequate mathematical models of heat and mass transfer. The paper proposed a formulation of the problem of melt motion in the framework of the Lagrangian description. The mathematical statement includes the balance equations for mass, momentum and energy, and physical equations for describing heat and mass transfer. Methods The smoothed particle hydrodynamics method was used for numerical simulation of the process of wire-based electron-beam surfacing on the substrate made from same materials (titanium or steel). A finite-difference analog of the equations is given and the algorithm for solving the problem is implemented. To integrate the discretized equations Verlet method was utilized. Algorithms are implemented in the open software package LAMMPS. Results The numerical simulation results allow the estimation of non-stationary volume temperature distributions, melt flow velocities and pressures, and characteristics of process. Conclusion The possibility of applying the developed mathematical model to describe additive production is shown. The comparison of numerical calculations with experimental studies showed good agreement.

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