On the connection between the spectral volume and the spectral difference method

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 T c which is the length of the time interval between successive exchange of boundary conditions. It is stable when T c is small and unstable when T c is large. For steady-state problems, the flux–velocity scheme converges faster than the other coupling schemes.