Stable and accurate integration schemes for coarse-grained dynamics
Abstract
Molecular Dynamics (MD) nowadays easily allows the simulation of systems composed of several millions of atoms for molecular systems. This is however still insufficient when interesting phenomena occur on space and time scales spanning several orders of magnitude. Coarse-grained models, which reduce the complexity of MD simulations with full atomistic details by representing some degrees of freedom in an average manner, are therefore of primary interest in this context. They allow the extension of the spatial scale by reducing the number of degrees of freedom, and also the temporal scales by increasing the admissible timesteps since mesoparticles interact via smoother potentials. The Dissipative Particle Dynamics is a particle-based coarse-grained model in which molecules are often represented by a single mesoscale particle. The time evolution of the mesoscale particles is governed by a stochastic differential equation. Dissipative and random forces take into account some effect of the missing degrees of freedom. However, Dissipative Particle Dynamics intrinsically is an equilibrium model, with a prescribed temperature, and cannot be used as such to study nonequilibrium systems. On the other hand, DPD with conserved energy (DPDE) is a model where the total energy of the system is preserved by introducing appropriate internal energies for the mesoscopic particles, which account for the energy of the degrees of freedom lost in the coarse-graining process. DPDE can be used to simulate shock and detonation waves. However, the efficient numerical integration of DPDE still requires some effort, in particular to devise easily highly-scalable numerical schemes for supercomputer architectures, which correctly preserve the energy, and are as stable and accurate as possible. Indeed, the current reference scheme in terms of accuracy is based on a pairwise splitting of the fluctuation/dissipation part of DPDE. It is therefore somewhat cumbersome to parallelize and does not allow for implementations compatible with the threadable character of new computing architectures. On the other hand, recent alternative schemes easier to parallelize may not be sufficiently accurate. The aim of this proposal is to devise more accurate integration schemes for DPDE, namely schemes such that the error for the average properties and transport coefficients (such as the mobility) scale as the square of the timestep. The underlying idea is to resort to a splitting of the dynamics between the Hamiltonian part (integrated with the Verlet algorithm, which is of order 2) and the fluctuation/dissipation, as done for standard Langevin dynamics. We will also pay particular attention to the stability of the resulting numerical methods. The schemes developed for DPDE can also be of interest for Smoothed Dissipative Particle Dynamics (SDPD), which is a mesoscopic variant of Smoothed Particle Hydrodynamics (SPH). It is a promising intermediate dynamics to couple microscopic dynamics such as DPDE and particle discretizations of Navier-Stokes equations such as SPH. This proposal complements the ongoing work at the Army Research Laboratory in the Weapons and Materials Research Directorate to modernize and optimize their suite of DPD methods in the highly-scalable LAMMPS software package. Through the construction of more efficient numerical schemes, the proposed work will provide performance enhancement to more efficiently utilize HPC resources and exploit emerging/heterogeneous HPC architectures, enabling simulations at previously inaccessible scales. This project supports numerous on-going ARL efforts aimed at developing science-based multiscale computational approaches leading towards predictive materials-by-design capability, including WMRD Mission programs, and the Collaborative Research Alliance ``Materials in Extreme Dynamic Environments .
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Jan 12, 2017
- Source ID
- W911NF1610254
Entities
People
- Gabriel Stoltz
Organizations
- Army Contracting Command
- United States Army
- École des Ponts ParisTech