Matthew K. Borg

Controllers for imposing continuum-to-molecular boundary conditions in arbitrary fluid flow geometries

We present a new parallelised controller for steering an arbitrary geometric region of a molecular dynamics (MD) simulation towards a desired thermodynamic and hydrodynamic state. We show that the controllers may be applied anywhere in the domain to set accurately an initial MD state, or solely at boundary regions to prescribe non-periodic boundary conditions (PBCs) in MD simulations. The mean molecular structure and velocity autocorrelation function remain unchanged (when sampled a few molecular diameters away from the constrained region) when compared with those distributions measured using PBCs. To demonstrate the capability of our new controllers, we apply them as non-PBCs in parallel to a complex MD mixing nano-channel and in a hybrid MD continuum simulation with a complex coupling region. The controller methodology is easily extendable to polyatomic MD fluids.

A multiscale method for micro/nano flows of high aspect ratio

We develop a new multiscale scheme for simulating micro/nano flows of high aspect ratio in the flow direction, e.g. within long ducts, tubes, or channels, of varying section. The scheme couples conventional hydrodynamic conservation equations for mass and momentum-flux with molecular dynamics (MD) in a unified framework. The method is very much different from common domain-decomposition hybrid methods, and is more related to micro-resolution methods, such as the Heterogeneous Multiscale Method. We optimise the use of the computationally-costly MD solvers by applying them only at a limited number of streamwise-distributed cross-sections of the macroscale geometry. The greater the streamwise scale of the geometry, the more significant is the computational speed-up when compared to a full MD simulation. We test our new multiscale method on the case of a converging/diverging nanochannel conveying a simple Lennard-Jones liquid. We validate the results from our simulations by comparing them to a full MD simulation of the same test case.

Water transport through carbon nanotubes with defects

Non-equilibrium molecular dynamics simulations are performed to investigate how changing the number of structural defects in the wall of a (7,7) single-walled carbon nanotube (CNT) affects water transport and internal fluid dynamics. Structural defects are modelled as vacancy sites (missing carbon atoms). We find that, while fluid flow rates exceed continuum expectations, increasing numbers of defects lead to significant reductions in fluid velocity and mass flow rate. The inclusion of such defects causes a reduction in the water density inside the nanotubes and disrupts the nearly frictionless water transport commonly attributed to CNTs.

Hybrid continuum-molecular modelling of multiscale internal gas flows

We develop and apply an efficient multiscale method for simulating a large class of low-speed internal rarefied gas flows. The method is an extension of the hybrid atomistic-continuum approach proposed by Borg et al. (2013) 28] for the simulation of micro/nano flows of high-aspect ratio. The major new extensions are: (1) incorporation of fluid compressibility; (2) implementation using the direct simulation Monte Carlo (DSMC) method for dilute rarefied gas flows, and (3) application to a broader range of geometries, including periodic, non-periodic, pressure-driven, gravity-driven and shear-driven internal flows. The multiscale method is applied to micro-scale gas flows through a periodic converging-diverging channel (driven by an external acceleration) and a non-periodic channel with a bend (driven by a pressure difference), as well as the flow between two eccentric cylinders (with the inner rotating relative to the outer). In all these cases there exists a wide variation of Knudsen number within the geometries, as well as substantial compressibility despite the Mach number being very low. For validation purposes, our multiscale simulation results are compared to those obtained from full-scale DSMC simulations: very close agreement is obtained in all cases for all flow variables considered. Our multiscale simulation is an order of magnitude more computationally efficient than the full-scale DSMC for the first and second test cases, and two orders of magnitude more efficient for the third case.

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.

Fluid simulations with atomistic resolution

We present a new hybrid method for simulating dense fluid systems that exhibit multiscale behaviour, in particular, systems in which a Navier-Stokes model may not be valid in parts of the computational domain. We apply molecular dynamics as a local microscopic refinement for correcting the Navier-Stokes constitutive approximation in the bulk of the domain, as well as providing a direct measurement of velocity slip at bounding surfaces. Our hybrid approach differs from existing techniques, such as the heterogeneous multiscale method (HMM), in some fundamental respects. In our method, the individual molecular solvers, which provide information to the macro model, are not coupled with the continuum grid at nodes (i.e. point-wise coupling), instead coupling occurs over distributed heterogeneous fields (here referred to as field-wise coupling). This affords two major advantages. Whereas point-wise coupled HMM is limited to regions of flow that are highly scale-separated in all spatial directions (i.e. where the state of non-equilibrium in the fluid can be adequately described by a single strain tensor and temperature gradient vector), our field-wise coupled HMM has no such limitations and so can be applied to flows with arbitrarily-varying degrees of scale separation (e.g. flow from a large reservoir into a nano-channel). The second major advantage is that the position of molecular elements does not need to be collocated with nodes of the continuum grid, which means that the resolution of the microscopic correction can be adjusted independently of the resolution of the continuum model. This in turn means the computational cost and accuracy of the molecular correction can be independently controlled and optimised. The macroscopic constraints on the individual molecular solvers are artificial body-force distributions, used in conjunction with standard periodicity. We test our hybrid method on the Poiseuille flow problem for both Newtonian (Lennard-Jones) and non-Newtonian (FENE) fluids. The multiscale results are validated with expensive full-scale molecular dynamics simulations of the same case. Very close agreement is obtained for all cases, with as few as two micro elements required to accurately capture both the Newtonian and non-Newtonian flowfields. Our multiscale method converges very quickly (within 3-4 iterations) and is an order of magnitude more computationally efficient than the full-scale simulation.

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.

Generation of initial molecular dynamics configurations in arbitrary geometries and in parallel

A computational pre-processing tool for generating initial configurations of molecules for molecular dynamics simulations in geometries described by a mesh of unstructured arbitrary polyhedra is described. The mesh is divided into separate zones and each can be filled with a single crystal lattice of atoms. Each zone is filled by creating an expanding cube of crystal unit cells, initiated from an anchor point for the lattice. Each unit cell places the appropriate atoms for the user-specified crystal structure and orientation. The cube expands until the entire zone is filled with the lattice; zones with concave and disconnected volumes may be filled. When the mesh is spatially decomposed into portions for distributed parallel processing, each portion may be filled independently, meaning that the entire molecular system never needs to fit onto a single processor, allowing very large systems to be created. The computational time required to fill a zone with molecules scales linearly with the number of cells in the zone for a fixed number of molecules, and better than linearly with the number of molecules for a fixed number of mesh cells. Our tool, molConfig, has been implemented in the open source C++ code OpenFOAM.

Boundary conditions for molecular dynamics simulations of water transport through nanotubes

This article compares both new and commonly used boundary conditions for generating pressure-driven water flows through carbon nanotubes in molecular dynamics simulations. Three systems are considered: (1) a finite carbon nanotube membrane with streamwise periodicity and ‘gravity’-type Gaussian forcing, (2) a non-periodic finite carbon nanotube membrane with reservoir pressure control, and (3) an infinite carbon nanotube with periodicity and ‘gravity’-type uniform forcing. Comparison between these focuses on the flow behaviour, in particular the mass flow rate and pressure gradient along the carbon nanotube, as well as the radial distribution of water density inside the carbon nanotube. Similar flow behaviour is observed in both membrane systems, with the level of user input required for such simulations found to be largely dependent on the state controllers selected for use in the reservoirs. While System 1 is simple to implement in common molecular dynamics codes, System 2 is more complicated, and the selection of control parameters is less straightforward. A large pressure difference is required between the water reservoirs in these systems to compensate for large pressure losses sustained at the entrance and exit of the nanotube. Despite a simple set-up and a dramatic increase in computational efficiency, the infinite length carbon nanotube in System 3 does not account for these significant inlet and outlet effects, meaning that a much smaller pressure gradient is required to achieve a specified mass flow rate. The infinite tube set-up also restricts natural flow development along the carbon nanotube due to the explicit control of the fluid. Observation of radial density profiles suggests that this results in over-constraint of the water molecules in the tube.

Asynchronous coupling of hybrid models for efficient simulation of multiscale systems

We present a new coupling approach for the time advancement of multi-physics models of multiscale systems. This extends the method of E et al. (2009) 5 to deal with an arbitrary number of models. Coupling is performed asynchronously, with each model being assigned its own timestep size. This enables accurate long timescale predictions to be made at the computational cost of the short timescale simulation. We propose a method for selecting appropriate timestep sizes based on the degree of scale separation that exists between models. A number of example applications are used for testing and benchmarking, including a comparison with experimental data of a thermally driven rarefied gas flow in a micro capillary. The multiscale simulation results are in very close agreement with the experimental data, but are produced almost 50,000 times faster than from a conventionally-coupled simulation.