Investigation of multiscale fluid flow characteristics based on a hybrid atomistic–continuum method

A computer program based on a molecular dynamics–continuum hybrid method has been developed in which the Navier–Stokes equations are solved in the continuum region and the molecular dynamics in the atomistic region. The coupling between the atomistic and continuum is constructed through constrained dynamics within an overlap region where both molecular and continuum equations are solved simultaneously. The simulation geometries are solved in three dimensions and an overlap region is introduced in two directions to improve the choice of using the molecular region in smaller areas. The proposed method is used to simulate steady and start-up Couette flow showing quantitative agreement with results from analytical solutions and full molecular dynamics simulations. The prepared algorithm and the computer code are capable of modeling fluid flows in micro and nano-scale geometries.     

Hybrid atomistic�Ccontinuum simulations of fluid flows involving interfaces

In this work, we use an hybrid atomistic–continuum (HAC) simulation method to study transient and steady isothermal flows of Lennard-Jones fluids near interfaces. Our hybrid method is based on a domain decomposition algorithm. The flow domain is composed of two overlapping regions: an atomistic region described by molecular dynamics, and a continuum region described by a finite volume discretization of the incompressible Navier–Stokes equations. To show the interest of such an hybrid method to compute flows near fluid/solid interface, we first applied our hybrid scheme to the classical Couette flow, where the moving wall is modelled at the atomistic scale. In addition, we also studied an oscillatory shear flow. Then, to compute flows near fluid/fluid interface, we applied our method to a two-phase Couette flow (liquid/gas), where the interface is modelled at the molecular scale. We show that hybrid results can sometimes differ from those provided by analytical solutions deduced from continuum mechanics equations combined with usual boundary/interface relations. For the Couette and oscillatory shear flows, a good agreement is found between hybrid simulations and macroscopic analytical solutions, however, we noticed that the fluid in contact with the wall can be more entailed than what expected. For the liquid/gas Couette flow, the hybrid simulation exhibits an unexpected jump of the velocity in the interfacial region, corresponding to a partial slip between the two fluid phases. Those interesting results highlight the interest of using an HAC method to deal with systems for which surfaces/interfaces effects are important.     

Molecular dynamics-based prediction of boundary slip of fluids in nanochannels

Computational modeling and simulation can provide an effective predictive capability for flow properties of the confined fluids in micro/nanoscales. In this paper, considering the boundary slip at the fluid–solid interface, the motion property of fluids confined in parallel-plate nanochannels are investigated to couple the atomistic regime to continuum. The corrected second-order slip boundary condition is used to solve the Navier–Stokes equations for confined fluids. Molecular dynamics simulations for Poiseuille flows are performed to study the influences of the strength of the solid–fluid coupling, the fluid temperature, and the density of the solid wall on the velocity slip at the fluid boundary. For weak solid–fluid coupling strength, high temperature of the confined fluid and high density of the solid wall, the large velocity slip at the fluid boundary can be obviously observed. The effectiveness of the corrected second-order slip boundary condition is demonstrated by comparing the velocity profiles of Poiseuille flows from MD simulations with that from continuum.     

A comparison of neural networks and adaptive neuro-fuzzy inference systems for the prediction of water diffusion through carbon nanotubes

Given the fact that artificial intelligence tools such as neural network and fuzzy logic are capable of learning and inferencing from the past to capture the patterns that exist in the data, this study presents an intelligent method for the forecasting of water diffusion through carbon nanotubes where predictions are generated from neuro-fuzzy structures using molecular dynamics data. Therefore, this research was mainly focused on combining molecular dynamics with artificial intelligence methods in order to reduce the computational time of biomolecular and nanofluidic simulations. Two different artificial intelligence methods are applied for the time-dependent water diffusion forecasting: artificial neural network (ANN) and adaptive neuro-fuzzy inference systems (ANFISs). The effects of different sizes of training sample sets on forecasting performance of ANN and ANFIS are investigated as well. Four different evaluation methods are used to measure the performance and forecasting accuracy of these two methods. As a result, ANFIS presents the higher accuracy than neural network method based on the comparison of these different evaluation methods adopted in this research. The results reported in this research demonstrate that combining of molecular dynamics with artificial intelligence methods can be one of the most powerful and beneficial tools for prediction of important nanofluidic parameters.     

Non-periodic Molecular Dynamics simulations of coarse grained lipid bilayer in water

We present a multiscale algorithm that couples coarse grained molecular dynamics (CGMD) with continuum solver. The coupling requires the imposition of non-periodic boundary conditions on the coarse grained Molecular Dynamics which, when not properly enforced, may result in spurious fluctuations of the material properties of the system represented by CGMD. In this paper we extend a control algorithm originally developed for atomistic simulations [3], to conduct simulations involving coarse grained water molecules without periodic boundary conditions. We demonstrate the applicability of our method in simulating more complex systems by performing a non-periodic Molecular Dynamics simulation of a DPPC lipid in liquid coarse grained water.     

A study on boundary force model used in multiscale simulations with non-periodic boundary condition

This paper presents an investigation of the non-periodic boundary condition (NPBC) which is often used in multiscale atomistic–continuum simulations. The relationship between the boundary force exerted by the imaginary atoms outside the atomistic domain and the fluid state parameters including density and temperature at the boundary is studied. A fitting formula of the boundary force as a function of the fluid state has been proposed based on the relationship. The accuracy of the fitting formula is verified by the equilibrium molecular dynamics (MD) simulations. Poiseuille flow with viscous dissipation and unsteady heat transfer between two walls is then simulated using the proposed fitting formula. The elimination of density oscillation near the boundary of atomistic region and good agreement of velocity and temperature evolutions with time from pure MD and the multiscale simulations adopting NPBC further confirm the correctness of our fitting formula.     

A block LU-SGS implicit unsteady incompressible flow solver on hybrid dynamic grids for 2D external bio-fluid simulations

A hybrid dynamic grid generation technique for two-dimensional (2D) morphing bodies and a block lower-upper symmetric Gauss-Seidel (BLU-SGS) implicit dual-time-stepping method for unsteady incompressible flows are presented for external bio-fluid simulations. To discretize the complicated computational domain around 2D morphing configurations such as fishes and insect/bird wings, the initial grids are generated by a hybrid grid strategy firstly. Body-fitted quadrilateral (quad) grids are generated first near solid bodies. An adaptive Cartesian mesh is then generated to cover the entire computational domain. Cartesian cells which overlap the quad grids are removed from the computational domain, and a gap is produced between the quad grids and the adaptive Cartesian grid. Finally triangular grids are used to fill this gap. During the unsteady movement of morphing bodies, the dynamic grids are generated by a coupling strategy of the interpolation method based on ‘Delaunay graph’ and local remeshing technique. With the motion of moving/morphing bodies, the grids are deformed according to the motion of morphing body boundaries firstly with the interpolation strategy based on ‘Delaunay graph’ proposed by Liu and Qin. Then the quality of deformed grids is checked. If the grids become too skewed, or even intersect each other, the grids are regenerated locally. After the local remeshing, the flow solution is interpolated from the old to the new grid. Based on the hybrid dynamic grid technique, an efficient implicit finite volume solver is set up also to solve the unsteady incompressible flows for external bio-fluid dynamics. The fully implicit equation is solved using a dual-time-stepping approach, coupling with the artificial compressibility method (ACM) for incompressible flows. In order to accelerate the convergence history in each sub-iteration, a block lower-upper symmetric Gauss-Seidel implicit method is introduced also into the solver. The hybrid dynamic grid generator is tested by a group of cases of morphing bodies, while the implicit unsteady solver is validated by typical unsteady incompressible flow case, and the results demonstrate the accuracy and efficiency of present solver. Finally, some applications for fish swimming and insect wing flapping are carried out to demonstrate the ability for 2D external bio-fluid simulations.     

Near-wall effects in micro scale Couette flow and heat transfer in the Maxwell-slip regimes

The effects of modified transport characteristics within an extremely thin layer adjacent to the fluid–solid interfaces are investigated for fully developed laminar micro-scale Couette flows with slip boundary conditions. The wall-adjacent layer effects are incorporated into the continuum-based mathematical model by imposing variable viscosity and thermal conductivity values close to the channel walls, for solving the momentum and energy conservation equations. Analytical expressions for the velocity profiles are derived and are subsequently utilized to obtain the temperature variations within the parallel plate channel, as a function of the significant system parameters. It is revealed that the variations in effective viscosity and thermal conductivity values within the wall-adjacent layer have profound influences on the fluid flow and the heat transfer characteristics within the channel, with an interesting interplay with the wall slip boundary conditions. These effects cannot otherwise be accurately captured by employing classical continuum based models for microscale Couette flows that do not take into account the alterations in effective transport properties within the wall adjacent layers.     

Multi-scale homogenization procedure for continuum–atomistic,thermo-mechanical problems

A multi-scale algorithm is developed for solving, continuum–atomistic thermo-mechanical problems. The coupling of the two scales occurs through a homogenization procedure. A uniform weighted residual approximation method is used to consistently model the interaction of the continuum and atomistic scales. Implementation of the coupling occurs through the transfer of macroscopic and microscopic variables at the macroscopic gauss points. The mechanism for transfer of atomistic information to the macro-level occurs through the Virial stress and the heat flux vector. A dynamic relaxation procedure is introduced to efficiently compute the coupled equilibrium solutions at the macroscopic and microscopic scales. The algorithm has been successfully tested for thermal stress analysis cases, involving constrained and unconstrained macro-components and fixed temperature distributions. Problems involving varying temperatures and heat transfer have been solved and are shown to be in good agreement with molecular dynamics results.     

A coupled Navier-Stokes/Vortex-Panel solver for the numerical analysis of wind turbines

The present paper introduces a coupled Navier-Stokes/Vortex-Panel solver for the computational study of incompressible high Reynolds number flow around horizontal axis wind turbines. The Navier-Stokes solver is confined to the near-field around one wind turbine blade; the Vortex-Panel method accounts for the far-field of a two-bladed rotor. A robust coupling between both methods is achieved through the spanwise distribution of bound circulation determined by Stokes’ theorem. The coupled solver reduces both artificial dissipation and computational cost compared to a full-domain Navier-Stokes analysis. Results obtained for inviscid and attached viscous flow around an optimal wind turbine blade are compared to a vortex model based on strip theory. Good agreement is found between both models that serves as a validation of the coupled solver for future applications to wind turbines.     

Analytic damping model for an MEM perforation cell

The concept of the perforation cell is specified for compact modelling of perforated gas dampers with micromechanical dimensions. Both, analytic expressions and FEM simulations, are used to derive its flow resistance. An extensive set of FEM simulations is performed to characterize the flow resistance of the cell, and to derive approximations for different flow regions by fitting simple functions to them. Sinusoidal small-amplitude velocities are assumed, and micromechanical dimensions are considered with rare gas effects in the slip flow regime (Knudsen number <0.1). The model is capable of modelling all practical combinations of the perforation cell dimensions in a wide range of perforation ratios (1,...,90%). Its validity is verified with a Navier–Stokes solver, and it is shown to be accurate (relative error <4.5%) in the continuum and slip flow regimes. Estimates for cut-off frequencies due to inertial and compressibility effects are specified in a way that the maximum operation frequency of the model can be easily tested. Using a harmonic FEM solver, these estimates are verified. The perforation cell model is also applied to estimate the damping in a perforated rectangular damper (4,...,64 square holes). The damping predicted by the simple model is in moderate agreement with that obtained with 3D FEM simulations.     

Integrated intelligent computing paradigm for the dynamics of micropolar fluid flow with heat transfer in a permeable walled channel

In this work, a novel application of bio-inspired computational heuristic paradigm is presented for micropolar fluid flow and heat transfer system in a channel with permeable walls by modeling competency of neural networks, global search of genetic algorithms, and rapid local convergence of sequential quadratic programming. Approximation theory in the mean squared error sense is exploited for the formulation of an objective function to solve the governing nonlinear fluidics system. The designed scheme is employed to study the dynamics of the model in terms of stream function, microrotation, concentration, and temperature profiles for prominent factors based on Reynolds number, Peclet number for diffusion of heat and mass, coupling, spin-gradient viscosity, micro inertia density parameters. The consistency and robustness of the solver are validated through statistical performance indices based on comparison with state of art Adams numerical method for accuracy and complexity measures.     

Three dimensional numerical simulations of long-span bridge aerodynamics, using block-iterative coupling and DES

The design of long-span bridges often depends on wind tunnel testing of sectional or full aeroelastic models. Some progress has been made to find a computational alternative to replace these physical tests. In this paper, an innovative computational fluid dynamics (CFD) method is presented, where the fluid-structure interaction (FSI) is solved through a self-developed code combined with an ANSYS-CFX solver. Then an improved CFD method based on block-iterative coupling is also proposed. This method can be readily used for two dimensional (2D) and three dimensional (3D) structure modelling. Detached-Eddy simulation for 3D viscous turbulent incompressible flow is applied to the 3D numerical analysis of bridge deck sections. Firstly, 2D numerical simulations of a thin airfoil demonstrate the accuracy of the present CFD method. Secondly, numerical simulations of a U-shape beam with both 2D and 3D modelling are conducted. The comparisons of aerodynamic force coefficients thus obtained with wind tunnel test results well meet the prediction that 3D CFD simulations are more accurate than 2D CFD simulations. Thirdly, 2D and 3D CFD simulations are performed for two generic bridge deck sections to produce their aerodynamic force coefficients and flutter derivatives. The computed values agree well with the available computational and wind tunnel test results. Once again, this demonstrates the accuracy of the proposed 3D CFD simulations. Finally, the 3D based wake flow vision is captured, which shows another advantage of 3D CFD simulations. All the simulation results demonstrate that the proposed 3D CFD method has good accuracy and significant benefits for aerodynamic analysis and computational FSI studies of long-span bridges and other slender structures.     

Concurrent coupling of atomistic and continuum models at finite temperature

A concurrent multiscale method for coupling discrete (atomistic) and continuum models at finite temperatures is presented. Motion of atoms is governed by an inter-atomic potential and is represented by molecular dynamics. A thermo-mechanical continuum defined by standard differential equations of conservation of momentum and heat transport is used. The coupling is performed by an interface region where the two models overlap. The phonon spectrum of the discrete region is divided into a low frequency part which is transferred to the continuum model as mechanical waves, and a high frequency component which is modeled in the continuum as diffusive heat transport. Seamless mechanical coupling is ensured by imposing weak compatibility of displacements in the interface region. The method is implemented in 1D and full bi-directional thermal and mechanical coupling is demonstrated in thermodynamic equilibrium and in non-equilibrium.     

Modeling of inhibition/excitation firing in olfactory bulb through spiking neurons

Spiking neural systems are based on biologically inspired neural models of computation since they take into account the precise timing of spike events and therefore are suitable to analyze dynamical aspects of neuronal signal transmission. These systems gained increasing interest because they are more sophisticated than simple neuron models found in artificial neural systems; they are closer to biophysical models of neurons, synapses, and related elements and their synchronized firing of neuronal assemblies could serve the brain as a code for feature binding and pattern segmentation. The simulations are designed to exemplify certain properties of the olfactory bulb (OB) dynamics and are based on an extension of the integrate-and-fire (IF) neuron, and the idea of locally coupled excitation and inhibition cells. We introduce the background theory to making an appropriate choice of model parameters. The following two forms of connectivity offering certain computational and analytical advantages, either through symmetry or statistical properties in the study of OB dynamics have been used:

• all-to-all coupling,
• receptive field style coupling.

Our simulations showed that the inter-neuron transmission delay controls the size of spatial variations of the input and also smoothes the network response. Our IF extended model proves to be a useful basis from which we can study more sophisticated features as complex pattern formation, and global stability and chaos of OB dynamics.     

Multi-solver algorithms for the partitioned simulation of fluid–structure interaction

In partitioned fluid–structure interaction simulations, the flow equations and the structural equations are solved separately. As a result, a coupling algorithm is needed to enforce the equilibrium on the fluid–structure interface in cases with strong interaction. This coupling algorithm performs coupling iterations between the solver of the flow equations and the solver of the structural equations. Current coupling algorithms couple one flow solver with one structural solver. Here, a new class of multi-solver quasi-Newton coupling algorithms for unsteady fluid–structure interaction simulations is presented. More than one flow solver and more than one structural solver are used for a single simulation. The numerical experiments demonstrate that the duration of a simulation decreases as the number of solvers is increased.     

Photorealistic visualization and fluid animation: coupling of Maya with a two-phase Navier-Stokes fluid solver

We have coupled the three-dimensional solver for the two-phase incompressible Navier-Stokes equations NaSt3DGPF with Autodesk Maya. Maya is the industry standard software framework for the creation of three-dimensional animations. The parallel level-set-based fluid solver NaSt3DGPF simulates the interaction of two fluids like air and water. It uses high-order finite difference discretization methods that are designed for physics applications. By coupling both applications, we are now able to set up scientific fluid simulations in an easy-to-use user interface. Moreover, the rendering techniques provided by Maya allow us to create photorealistic visualizations for computational fluid dynamics problems and support the creation of highly visually realistic fluid simulations for animation movies. Altogether, we obtain an easy usable and fully coupled fluid animation toolkit for two-phase fluid simulations. These are the first published results of the full integration of a physics-oriented, high-order grid-based parallel two-phase fluid solver in Maya, at least to our knowledge.     

Coupled 3D master equation and 1D drift‐diffusion approach for advanced OLED modeling

A novel simulation approach for excitonic organic light‐emitting diodes (OLEDs) is established by combining a continuous one‐dimensional (1D) drift‐diffusion (DD) model for the charge carrier dynamics with a three‐dimensional (3D) master equation (ME) model describing the exciton dynamics in a multilayer OLED stack with an additional coupling to a thin‐film optics solver. This approach effectively combines the computational efficiency of the 1D DD solver with the physical accuracy of a discrete 3D ME model, where excitonic long‐range interactions for energy transfer can be taken into account. The coupling is established through different possible charge recombination types as well as the carrier densities themselves. We show that such a hybrid approach can efficiently and accurately describe steady‐state and transient behavior of optoelectronic devices reported in literature. Such a tool will facilitate the optimization and characterization of multilayer OLEDs and other organic semiconductor devices.     

Suspended sediment load simulation by two artificial neural network methods using hydrometeorological data

Estimates of sediment load are required in a wide spectrum of water resources engineering problems. The nonlinear nature of suspended sediment load series necessitates the utilization of nonlinear methods for simulating the suspended sediment load. In this study artificial neural networks (ANNs) are employed to estimate the daily total suspended sediment load on rivers. Two different ANN algorithms, the feed-forward back-propagation (FFBP) method and the radial basis functions (RBF), were used for this purpose. The neural networks are trained using rainfall flow and suspended sediment load data from the Juniata Catchment, USA. The simulations provided satisfactory simulations in terms of the selected performance criteria comparing well with conventional multi-linear regression. Similarly, the simulated sediment load hydrographs obtained by two ANN methods are found closer to the observed ones again compared with multi-linear regression.