Molecular dynamics three-dimensional simulations of the dispersed system dynamics at the molecular level

Victor Malyshev, Elena Moiseeva, Dmitriy Marin, Nail Gumerov, Constantin Mikhaylenko

Objective:

The molecular dynamics simulations in the application to the study of the bubble nucleation in water under negative pressure in the presence of the nanoscale impurities

Vapor bubble nucleation in water

Water droplet formation in a vacuum

Water droplet on the platinum surface

Molecular dynamics (MD) is a computer simulation of the dynamics of the single-phase and multi-phase systems. It is based on the idea that all the particles follow the trajectories derived from the equations of motion. Molecular dynamics simulations are used for modeling the processes at micro- and nanoscale when the classical continuum models could not be applied because of the extremely small amount of the molecules in the system.

Molecular dynamics simulations require considerable computational resources, dramatically increasing with the growth of the system size. In the direct mathematical formulation, the computations of all the forces acting on the particles require the solving of the system of linear algebraic equations, the amount of which is defined by the number of atoms. It is known, that the algorithmic complexity of the direct method is of the order of magnitude O(N2).

The use of the modern high-performance computational algorithms allow to reduce the complexity. Thus, the computation of the forces, defined by the Lennard-Jones potential, has the complexity O(NlogN) when using the special data structures. The calculations of the far-field forces, defined by the Coulomb potential, can be accelerated using the Fast Multipole method (FMM). FMM allows one to decrease the complexity to O(N). The latter is particularly important for the simulations of the water molecules, because the 3/4 of all the intermolecular interactions are determined by the Coulomb potential.

Further decrease of the computational time is achieved by the use of modern hardware, such as high-performance computing GPU (Graphics Processing Unit, GPU). Currently, the calculations of one time step for a system of 1000000 water molecules take 30 seconds on a personal computer equipped with two Intel Xeon processors and computer graphics card NVidia Tesla 2050. For a characteristic time step of 10 femtoseconds, the computational performance of 1 picoseconds per hour can be achieved for the simulations of a system of one million water molecules.

Prospects:

Further application of the method developed and the software based on it will produce a mathematical modeling of the micro-and nanoscale vapor bubbles nucleation in water in the presence of gold nanoparticles. The results can be used for further experimental study of these processes