Book
Smart Innovation, Systems and Technologies, Proceedings of the International Conference on Computational Methods in Continuum Mechanics (CMCM 2021), Volume 2
We discuss the applicability of multiphase lattice Boltzmann method for the simulation of the drop
oscillation. We demonstrate that the simulation of the single drop excited to the first eigenmode does
follow Rayleigh formula. Simulations show no sensitivity to the number of the discrete velocities with
D3Q19 and D3Q27 representations of the distribution function in three dimensions. The boundaries do
influent the motion of the drop—division of the computational area by the even and the odd number of
cells comes out important and leads to symmetry violence. The second part of the chapter describes the
oscillations of the ensemble of three drops due to the excitation of the central drop in the first eigenmode.
The motion of the backdrops does strongly depend on the viscosity of the fluid. We provide future details
of simulations.
The classical problem of oscillations of liquid droplets is a good test for the applicability of computer simulation. We discuss the details of our approach to a simulation scheme based on the Boltzmann lattice equation. We show the results of modeling induced vibrations in a chain of three drops in a closed tube. In the initial position, the central drop has formed as an ellipsoid, out of the spherical equilibrium form. The excitation of vibrations in the left and right droplets depends on the viscosity of the surrounding fluid and the surface tension. Droplets are moving out of the initial position as well. We discuss the limits of the applicability of our model for the study of such a problem. We will also show the dynamics of the simulated process.
Lattice Boltzmann method is a mesoscopic method used for solving hydrodynamics problems of both incompressible and compressible fluids. Although the method is widely used, reliability of the results is unclear. Therefore, we use the method to solve a fundamental problem with a known analytical solution, the Couette flow. We estimate the accuracy of the simulation results obtained by setting different types of spatial grids, boundary conditions, and equilibrium distribution functions. However, the method imposes restrictions on a large number of simulation parameters such as Reynolds and Mach numbers. During simulation we discovered an unexpected behavior of the solution using classical lattice Boltzmann method. In these simulations we find that the conservation law is violated due to an unexpected inflow in the upper corners of the computational domain.
We simulate the oscillation of the viscous drop in the viscous liquid. We combine methods of chromodynamics model and Shan-Chen pseudo-potential for the immiscible fluids. We measure the frequency of the first nontrivial eigenmode using the initial ellipsoid form of the drop. Drop oscillates about the equilibrium spherical form of radius $R$. Computed frequency as a function of the radius $R$ follows to the well known Rayleigh formula. We discuss the simulation setup in the framework of the Lattice Boltzmann method.
The stability of the quasi-two-dimensional droplet flow is of great importance in microfluidic devices. We check the drop's stability in the square box using the immersed boundary and lattice Boltzmann methods. We implement two-dimensional equations within the immersed boundary approach in the Palabos programming platform. We check the influence of the boundaries on the drop movement. We estimate fluctuations in the quantities while applying different initial conditions of the linear and angular velocities. We found that the level of fluctuations depends on the symmetrical displacement of drop at the initial state. The effect is connected with the hydrodynamic interaction of drop with the walls.
The dynamics of a two-component Davydov-Scott (DS) soliton with a small mismatch of the initial location or velocity of the high-frequency (HF) component was investigated within the framework of the Zakharov-type system of two coupled equations for the HF and low-frequency (LF) fields. In this system, the HF field is described by the linear Schrödinger equation with the potential generated by the LF component varying in time and space. The LF component in this system is described by the Korteweg-de Vries equation with a term of quadratic influence of the HF field on the LF field. The frequency of the DS soliton`s component oscillation was found analytically using the balance equation. The perturbed DS soliton was shown to be stable. The analytical results were confirmed by numerical simulations.
Radiation conditions are described for various space regions, radiation-induced effects in spacecraft materials and equipment components are considered and information on theoretical, computational, and experimental methods for studying radiation effects are presented. The peculiarities of radiation effects on nanostructures and some problems related to modeling and radiation testing of such structures are considered.