Heterogeneous multiscale method for high energy-density matter: Connecting kinetic theory and molecular dynamics

We have developed a concurrent heterogeneous multiscale method (HMM) framework with a microscale molecular dynamics (MD) model and a macroscale kinetic Vlasov-BGK model. The kinetic model is formulated such that BGK collision times are the closure data obtained from MD. Using the H-theorem, we develop the mathematical link between the MD and the kinetic model. We examine three relaxation processes, energy, momentum, and bump-on-tail, using full microscale MD simulations as a reference solution. We find that solutions computed with the HMM framework offer a significant computational reduction ($14\times -100\times$) compared with computing a full MD solution, with significant improvements in accuracy compared with a kinetic model using analytical collision times.