Multiscale Multilevel Approach to Solution of Nanotechnology Problems

Sergey Polyakov,Viktoriia Podryga,Gh Adam,D Podgainy,J Buša,M Hnatič

doi:10.1051/epjconf/201817301010

Abstract

The paper is devoted to a multiscale multilevel approach for the solution of nanotechnology problems on supercomputer systems. The approach uses the combination of continuum mechanics models and the Newton dynamics for individual particles. This combination includes three scale levels: macroscopic, mesoscopic and microscopic. For gas–metal technical systems the following models are used. The quasihydrodynamic system of equations is used as a mathematical model at the macrolevel for gas and solid states. The system of Newton equations is used as a mathematical model at the mesoand microlevels; it is written for nanoparticles of the medium and larger particles moving in the medium. The numerical implementation of the approach is based on the method of splitting into physical processes. The quasihydrodynamic equations are solved by the finite volume method on grids of different types. The Newton equations of motion are solved by Verlet integration in each cell of the grid independently or in groups of connected cells. In the framework of the general methodology, four classes of algorithms and methods of their parallelization are provided. The parallelization uses the principles of geometric parallelism and the efficient partitioning of the computational domain. A special dynamic algorithm is used for load balancing the solvers. The testing of the developed approach was made by the example of the nitrogen outflow from a balloon with high pressure to a vacuum chamber through a micronozzle and a microchannel. The obtained results confirm the high efficiency of the developed methodology.

Highlights

The modern computing allows modeling very large and complex systems and processes
One of the modern and actively developing approaches to solving such problems is the multiscale approach which combines the methods of the continuum mechanics (MCM) and the Newton dynamics for individual particles
At the molecular level it allows to determine the parameters of the equation of state of a real gas [7], to calculate the kinetic properties of the gas [8], to determine the type of the boundary conditions at the walls of the microchannel [5, 6]. This approach is based on a combination of MCM and Newton dynamics for individual particles and includes two levels of modeling: macroscopic and microscopic

Summary

Introduction

The modern computing allows modeling very large and complex systems and processes. Computer modeling has become one of the most effective tools in many branches of science and production. At the molecular level it allows to determine the parameters of the equation of state of a real gas [7], to calculate the kinetic properties of the gas [8], to determine the type of the boundary conditions at the walls of the microchannel [5, 6]. This approach is based on a combination of MCM and Newton dynamics for individual particles and includes two levels of modeling: macroscopic and microscopic. The consideration of the mesoscopic level allows to track the detailed behavior of the individual large particles, for example, during their deposition on a substrate in order to create a given spatial nanostructure

Mathematical formulation

Numerical approach

Algorithms and program implementation

Calculation results

Conclusion