The coupling of element-free Galerkin method and molecular dynamics for the incompressible flow problems

Abstract

The coupling between the macro-scale numerical method and the molecular dynamics (MD) simulation is developed for simulating the micro- and nano-scale incompressible flow problems. The proposed coupling schemes are based on the technique of “domain decomposition” in which the MD simulation is used in the region where molecular details are important, while the macro-scale numerical method is used in the remaining bulk region. These two different descriptions are matched in an overlap region where we ensure the continuity of mass, momentum, energy, and their fluxes. Especially, in order to take full advantage of meshfree methods, the element-free Galerkin (EFG) method is adopted as the macro-scale numerical method and the variational multiscale method is introduced to overcome the numerical instabilities of the EFG method for solving the incompressible flow problems. Finally, we apply the coupling to solve the isothermal and non-isothermal Couette flow problems. The numerical results indicate that there is a good agreement between the results of the macro-scale numerical method and the results of the MD simulation in the overlap region. In addition, due to that the MD simulation is used in the region where the micro-effects are important, then we can simulate out the micro-scale effects in this crucial region.