Analytical and numerical study of coupled atomistic-continuum methods for fluids

The stability and convergence rate of coupled atomistic-continuum methods are studied analytically and numerically. These methods couple a continuum model with molecular dynamics through the exchange of boundary conditions in the continuum-particle overlapping region. Different coupling schemes, including velocity–velocity, flux–velocity, velocity–flux and flux–flux, are studied. It is found that the velocity–velocity and flux–velocity schemes are stable. The flux–flux scheme is weakly unstable. The stability of the velocity–flux scheme depends on the parameter TcTc which is the length of the time interval between successive exchange of boundary conditions. It is stable when TcTc is small and unstable when TcTc is large. For steady-state problems, the flux–velocity scheme converges faster than the other coupling schemes.