Collision dynamics numerical techniques

The algorithm of lamella stabilization is a key technique in the numerical simulation. At high Weber numbers extremely thin lamellae appear in droplet collisions. If an insufficient fine mesh is used in the simulatimi, the lamella can rupture which leads to wrong results. The idea to circumvent the problem is to prevent the curvature computation in the lamella region from being affected by the opposite lamella surface. Both in the cases of head-on and off-center collisions, our developed algorithm of lamella stabilization avoids the numerical rupture of a lamella and is able to capture the collision dynamics in agreement with experiment. 

Ge and Fan (2005) developed a 3-D numerical model based on the level-set method and finite-volume technique to simulate the saturated droplet impact on a superheated flat surface. A 2-D vapor-flow model was coupled with the heat-transfer model to account for the vapor-flow dynamics caused by the Leidenfrost evaporation. The droplet is assumed to be spherical before the collision and the liquid is assumed to be incompressible. 

Abstract Among the noncontinuum-based computational techniques, the lattice Boltzman method (LBM) has received considerable attention recently. In this chapter, we will briefly present the main elements of the LBM, which has evolved as a minimal kinetic method for fluid dynamics, focusing in particular, on multiphase flow modeling. We will then discuss some of its recent developments based on the multiple-relaxation-time formulation and consistent discretizatirai strategies for enhanced numerical stability, high viscosity contrasts, and density ratios for simulation of interfacial instabilities and multiphase flow problems. As examples, numerical investigations of drop collisions, jet break-up, and drop impact on walls will be presented. We will also outline some future directions for further development of the LBM for applications related to interfacial instabilities and sprays. 

The lattice Boltzmann method (LBM) is a relatively new simulation technique for complex fluid systems and has attracted great interests from researchers in computational physics and engineering. Unlike traditional computation fluid dynamics (CFD) methods to numerically solve the conservation equations of macroscopic properties (i.e., mass, momentum, and energy), LBM models the fluid as fictitious particles, and such particles perform consecutive propagation and collision processes over a discrete lattice mesh. Due to its particulate nature and local dynamics, LBM has several advantages over conventional CFD methods, especially in dealing with complex boundaries, incorporation of microscopic interactions, and parallel computation [1, 2]. 

The Boltzmann equation must be solved with appropriate boundary conditions to obtain f and f. The full Boltzmann equation has not been solved analytically or numerically. Current approximate methods for extracting the desired information from the Boltzmann equation are covered in detail in a recent reference [2.84]. In view of this review, discussion of these methods will not be given. It is sufficient to indicate some of the principal methods which have been employed. These are moment or integral methods for specific molecular scattering laws, the use of "models" (of which the BGK model is the simplest) for the collisions term J(fgfg), and direct simulation by Monte Carlo or molecular-dynamics techniques. 

MD simulations involve numerical determinations of individual trajectories, that is, solutions to Newton s equation of motion for particular initial conditions. In chemistry, this technique began with the study of individual gas-phase collisions, where large numbers of trajectories were run to explicitly average over initial conditions. For macromolecules or liquid simulations, however, the frequency of atomic collisions becomes so great that simulations often appear to be ergodic, such that a single trajectory samples phase space with the same distribution as do multiple simulations with randomized starting points. This implies that a dynamics simulation can be used to explore phase space and make connections to classical thermodynamics and kinetics. 

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