A study on boundary force model used in multiscale simulations with non-periodic boundary condition

This paper presents an investigation of the non-periodic boundary condition (NPBC) which is often used in multiscale atomistic–continuum simulations. The relationship between the boundary force exerted by the imaginary atoms outside the atomistic domain and the fluid state parameters including density and temperature at the boundary is studied. A fitting formula of the boundary force as a function of the fluid state has been proposed based on the relationship. The accuracy of the fitting formula is verified by the equilibrium molecular dynamics (MD) simulations. Poiseuille flow with viscous dissipation and unsteady heat transfer between two walls is then simulated using the proposed fitting formula. The elimination of density oscillation near the boundary of atomistic region and good agreement of velocity and temperature evolutions with time from pure MD and the multiscale simulations adopting NPBC further confirm the correctness of our fitting formula.