Coupled continuum hydrodynamics and molecular dynamics method for multiscale simulation

We present a new hybrid methodology for carrying out multiscale simulations of flow problems lying between continuum hydrodynamics and molecular dynamics, where macro/micro lengthscale separation exists only in one direction. Our multiscale method consists of an iterative technique that couples mass and momentum flux between macro and micro domains, and is tested on a converging/diverging nanochannel case containing flow of a simple Lennard-Jones liquid. Comparisons agree well with a full MD simulation of the same test case

The FADE mass-stat:A technique for inserting or deleting particles in molecular dynamics simulations

The emergence of new applications of molecular dynamics (MD) simulation calls for the development of mass-statting procedures that insert or delete particles on-the-fly. In this paper we present a new mass-stat which we term FADE, because it gradually “fades-in” (inserts) or “fades-out” (deletes) molecules over a short relaxation period within a MD simulation. FADE applies a time-weighted relaxation to the intermolecular pair forces between the inserting/deleting molecule and any neighbouring molecules. The weighting function we propose in this paper is a piece-wise polynomial that can be described entirely by two parameters: the relaxation time scale and the order of the polynomial. FADE inherently conserves overall system momentum independent of the form of the weighting function. We demonstrate various simulations of insertions of atomic argon, polyatomic TIP4P water, polymer strands, and C60 Buckminsterfullerene molecules. We propose FADE parameters and a maximum density variation per insertion-instance that restricts spurious potential energy changes entering the system within desired tolerances. We also demonstrate in this paper that FADE compares very well to an existing insertion algorithm called USHER, in terms of accuracy, insertion rate (in dense fluids), and computational efficiency. The USHER algorithm is applicable to monatomic and water molecules only, but we demonstrate that FADE can be generally applied to various forms and sizes of molecules, such as polymeric molecules of long aspect ratio, and spherical carbon fullerenes with hollow interiors

Water transport through (7,7) carbon nanotubes of different lengths using molecular dynamics

Non-equilibrium molecular dynamics simulations are used to investigate water transport through (7,7) CNTs, examining how changing the CNT length affects the internal flow dynamics. Pressure-driven water flow through CNT lengths ranging from 2.5 to 50 nm is simulated. We show that under the same applied pressure difference an increase in CNT length has a negligible effect on the resulting mass flow rate and fluid flow velocity. Flow enhancements over hydrodynamic expectations are directly proportional to the CNT length. Axial profiles of fluid properties demonstrate that entrance and exit effects are significant in the transport of water along CNTs. Large viscous losses in these entrance/exit regions lead into central “developed” regions in longer CNTs where the flow is effectively frictionless

A Laplacian-based algorithm for non-isothermal atomistic-continuum hybrid simulation of micro and nano-flows

We propose a new hybrid algorithm for incompressible micro and nanoflows that applies to non-isothermal steady-state flows and does not require the calculation of the Irving–Kirkwood stress tensor or heat flux vector. The method is validated by simulating the flow in a channel under the effect of a gravity-like force with bounding walls at two different temperatures and velocities. The model shows very accurate results compared to benchmark full MD simulations. In the temperature results, in particular, the contribution of viscous dissipation is correctly evaluated

Exploiting timescale separation in micro and nano flows

In this paper we describe how timescale separation in micro/nano flows can be exploited for computational acceleration. A modified version of the seamless heterogenous multiscale method (SHMM) is proposed: a multi-step SHMM. This maintains the main advantages of SHMM (e.g., re-initialisation of micro data is not required; temporal gearing (computational speed-up) is easily controlled; and it is applicable to full and intermediate degrees of timescale separation) while improving on accuracy and greatly reducing the number of macroscopic computations and micro/macro coupling instances required. The improved accuracy of the multi-step SHMM is demonstrated for two canonical one-dimensional transient flows (oscillatory Poiseuille and oscillatory Couette flow) and for rarefied-gas oscillatory Poiseuille flow

Time-step coupling for hybrid simulations of multiscale flows

A new method is presented for the exploitation of time-scale separation in hybrid continuum-molecular models of multiscale flows. Our method is a generalisation of existing approaches, and is evaluated in terms of computational efficiency and physical/numerical error. Comparison with existing schemes demonstrates comparable, or much improved, physical accuracy, at comparable, or far greater, efficiency (in terms of the number of time-step operations required to cover the same physical time). A leapfrog coupling is proposed between the ‘macro’ and ‘micro’ components of the hybrid model and demonstrates potential for improved numerical accuracy over a standard simultaneous approach. A general algorithm for a coupled time step is presented. Three test cases are considered where the degree of time-scale separation naturally varies during the course of the simulation. First, the step response of a second-order system composed of two linearly-coupled ODEs. Second, a micro-jet actuator combining a kinetic treatment in a small flow region where rarefaction is important with a simple ODE enforcing mass conservation in a much larger spatial region. Finally, the transient start-up flow of a journal bearing with a cylindrical rarefied gas layer. Our new time-stepping method consistently demonstrates as good as or better performance than existing schemes. This superior overall performance is due to an adaptability inherent in the method, which allows the most-desirable aspects of existing schemes to be applied only in the appropriate conditions