Multiple Length/Time Scale Modeling of Multi-physics
Jiaoyan Li (The George Washington University), James Lee (George Washington University)
From Atomistics to Reality: Spanning Scales in Simulations and Experiments Symposium A
Mon 4:20 - 5:40
CIT 165
Molecular dynamics (MD) has established itself as a widely employed discipline for the study of material behaviors at atomic level. For the modeling of multi-physics, i.e., thermomechanical-electromagnetic coupling phenomena, we recast the governing equations for atoms by reformulating the Nose-Hoover thermostat and by incorporating with the Maxwell’s equations at atomic level. However, we realize that the extension of MD into computational science over a realistic range of length is limited, due to the large number of particles involved as well as the complex nature of their interactions. The limitations are also imposed by the requirement of smallness of the time step, and yet one is interested in events that occur over a much longer time scale. To expand the realm of modeling and simulation, we propose a multiple length/time scale approach along with the employment of massively parallel computing technique. Our philosophy is that the solution region can be and should be decomposed into two kinds of sub-regions in space. For the critical region (named atomic region) modeled by MD simulation, a relatively small time step is used to update the solutions; for the far field (named atom-based continuum region), we adopt a kinematic constraint and rigorously derive a coarse-grained MD, which allows for a relatively large time step and has a much better efficiency. In this work, we will demonstrate that a small-deformation approximation will further reduce the computational efforts and result in an atom-based continuum theory. Based on the above-mentioned theoretical framework, we have also developed a corresponding computer code for numerical investigations. The numerical results can show (i) the wave propagations in acoustic mode and optical mode, (ii) the heat conduction process, (iii) the material responses when it is subjected to external electromagnetic fields, and (iv) the induced polarization, voltage, electrical field and magnetic field, etc.