Simulation Of Complex Fluids Research Articles

Energy-stable auxiliary variable viscosity splitting (AVVS) method for the incompressible Navier–Stokes equations and turbidity current system

In this work, we develop a novel energy-stable linear approach, which we name as auxiliary variable viscosity splitting (AVVS) method, to efficiently solve the incompressible fluid flows. Different from the projection-type methods with pressure correction, the AVVS method adopts the viscosity splitting strategy to split the original momentum equation into an intermediate momentum equation without divergence-free constraint and an advection-free momentum equation. A time-dependent auxiliary variable which has exact value 1 is introduced to construct a supplementary equation. The new model not only inherits the same dynamics of original incompressible Navier–Stokes equations, but also facilitates us to design linearly decoupled and energy-stable time-marching scheme. Comparing with the conventional projection-type schemes, the present method leads to an energy dissipation law with respect to kinetic energy instead of a modified energy including velocity and pressure gradient. In each time step, only two parabolic equations with constant coefficients and one Poisson equation need to be solved. Therefore, the numerical implementation is highly efficient. Moreover, the proposed AVVS method can be directly extended to construct linear, decoupled, and energy-stable scheme for the turbidity current system with slight modifications on the right-hand side of supplementary equation. Extensive numerical experiments are implemented to validate the accuracy, energy stability, and capability in complex fluid simulations.

On floating point precision in computational fluid dynamics using OpenFOAM

Thanks to the computational power of modern cluster machines, numerical simulations can provide, with an unprecedented level of details, new insights into fluid mechanics. However, taking full advantage of this hardware remains challenging since data communication remains a significant bottleneck to reaching peak performances. Reducing floating point precision is a simple and effective way to reduce data movement and improve the computational speed of most applications. Nevertheless, special care needs to be taken to ensure the quality and convergence of computed solutions, especially when dealing with complex fluid simulations. In this work, we analyse the impact of reduced (single and mixed compared to double) precision on computational performance and accuracy for computational fluid dynamics. Using the open source library OpenFOAM, we consider incompressible, compressible, and multiphase fluid solvers for testing on relevant benchmarks for flows in the laminar and turbulent regime and in the presence of shock waves. Computational gain and changes in the scalability of applications in reduced precision are also discussed. In particular, an ad hoc theoretical model for the strong scaling allows us to interpret and understand the observed behaviours, as a function of floating point precision and hardware specifics. Finally, we show how reduced precision can significantly speed up a hybrid CPU–GPU implementation, made available to OpenFOAM end-users recently, that simply relies on a GPU linear algebra solver developed by hardware vendors.

Field-theoretic simulations beyond δ-interactions: Overcoming the inverse potential problem in auxiliary field models.

Modern field-theoretic simulations of complex fluids and polymers are constructed around a particle-to-field transformation that brings an inverse potential u-1 in the model equations. This has restricted the application of the framework to systems characterized by relatively simple pairwise interatomic interactions; for example, excluded volume effects are treated through the use of δ-function interactions. In this study, we first review available nonbonded pair interactions in field-theoretic models and propose a classification. Then, we outline the inverse potential problem and present an alternative approach on the basis of a saddle-point approximation, enabling the use of a richer set of pair interaction functions. We test our approach by using as an example the Morse potential, which finds extensive applications in particle-based simulations, and we calibrate u-1 with results from a molecular dynamics simulation. The u-1 thus obtained is consistent with the field-theoretic model equations, and when used in stand-alone self-consistent field simulations, it produces the correct fluid structure starting from a random initial state of the density field.

Simulation of high Schmidt number fluids with dissipative particle dynamics: Parameter identification and robust viscosity evaluation

Dissipative particle dynamics (DPD) is a widely used coarse-grained technique for the simulation of complex fluids. Although the method is capable of describing the hydrodynamics of any fluid, the common choice of DPD parameters, such as friction coefficient γ, dissipative cutoff radius rcD, coarse-graining factor Nm and weighting function exponent s, unrealistically leads to the simulation of liquid water with a low Schmidt number Sc at standard pressure and temperature. In this work we explored the influence of these parameters, finding the set of parameters needed to properly simulate liquid water. Particular attention was devoted to the numerical techniques to calculate the transport properties from equilibrium simulations, especially in the calculation of the viscosity, comparing the most commonly adopted techniques and formulating a recipe that can be used for further investigations.

Active- and transfer-learning applied to microscale-macroscale coupling to simulate viscoelastic flows

Active- and transfer-learning are applied to microscale dynamics of polymer flows for the multiscale discovery of effective constitutive approximations required in viscoelastic flow simulation. The result is macroscopic rheology directly connected to a microstructural model. Micro and macroscale simulations are adaptively coupled by means of Gaussian process regression (GPR) to run the expensive microscale computations only as necessary. This multiscale method is demonstrated with flows of a polymer solution as a model system. At the microscale level dissipative particle dynamics (DPD) is employed to model the fluid as a suspension of bead-spring micro-structures subjected to steady shear flow. The results yield the non-Newtonian viscosity and the first normal stress difference at strain rates as training data used in a GPR model. DPD parameters are calibrated with respect to experimental data for a real polymer solution. Compliance with these data requires adjustment of the DPD model's cutoff radius, which then becomes a function of the second invariant of the strain rate tensor. The FENE-P model is chosen for the macroscale description using the spectral element method (SEM) to simulate channel flow and flow past a circular cylinder. The DPD results at the lowest possible shear strain rate yield an estimate of the zero-shear rate viscosity, which allows the initiation of the macroscale flow by SEM as a Newtonian fluid. The resulting strain-rate field is surveyed to determine additional shear strain rate sampling points for the DPD system. This new information allows an initial fitting of parameters of the constitutive equation followed by new SEM simulations at the macroscale. Guided by active-learning GPR to select new sampling points, this process continues until convergence is achieved.The effectiveness of this new simulation paradigm for viscoelastic flows is tested with different macroscale operating conditions. The effective closure learned in the channel simulation is then transferred directly to the flow past a circular cylinder at low Reynolds number, where the results show that only two additional DPD simulations are required to achieve a satisfactory constitutive model. With an increase of the Reynolds number, the active-learning scheme automatically detects the inaccuracy of the learned constitutive model, and initiates additional DPD simulations for the extra data needed to once again close the microscale-macroscale coupled system. This new paradigm of active- and transfer-learning for multiscale modeling is readily applicable to other microscale-macroscale coupled simulations of complex fluids and other materials. Furthermore, the coupling between microscale and macroscale solvers can be seamlessly implemented with our open source multiscale universal interface (MUI) library.

Exploring the Molecular Distributions in Dilute Polymer Solutions Using a Multi-Scale Numerical Solver.

Simulating the rheological behaviors of polymer solutions is intrinsically a multi-scale problem. To study the macroscopic and microscopic characteristics in the fluid flow of dilute polymer solutions, we designed a multi-scale solver, which couples the Brownian Configuration Fields with the macroscopic hydrodynamic governing equations. Numerical simulation results using the multi-scale solver exhibited good accordance with the macroscopic only approach. Through a scalar field D we also quantitatively studied the flow behaviours in 2D planar channels, and analyzed the correlation between the molecular distribution and the macroscopic fluid flow in polymer solutions. Our results verified the correctness of the solver, which could provide valuable guidance for multi-scale simulations of complex fluids based on OpenFOAM.

Effect of time step size on configurational temperature accuracy in dissipative particle dynamics simulation of complex fluids

Effect of time step size on configurational temperature accuracy in dissipative particle dynamics simulation of complex fluids

A mesoscopic simulation of material ---Advances in Dissipative particle dynamics research

A mesoscopic simulation of material --Dissipative particle dynamics(DPD), as the bond between macroscopic and microscopic simulation, had been increasingly draw attention in the research of soft matters, including the flowing condition and the morphological structure. The method of DPD simulation had been applied extensively in the fields of soft matters such as biomacromolecule and the flows of polymers since the DPD simulation has an advantage in time and space scale. In this article, the origin, the theoretical model and the development of dissipative particle dynamics are introduced at first. Subsequently, the advances in the simulation of complex fluids and polymers are reviewed. Finally, the future development and application are concluded.

Scaling features of the tribology of polymer brushes of increasing grafting density around the mushroom-to-brush transition.

Nonequilibrium coarse-grained, dissipative particle dynamics simulations of complex fluids, made up of polymer brushes tethered to planar surfaces immersed in a solvent yield nonmonotonic behavior of the friction coefficient as a function of the polymer grating density on the substrates, Γ, while the viscosity shows a monotonically increasing dependence on Γ. This effect is shown to be independent of the degree of polymerization, N, and the size of the system. It arises from the composition and the structure of the first particle layer adjacent to each surface that results from the confinement of the fluid. Whenever such layers are made up of as close a proportion of polymer beads to solvent particles as there are in the fluid, the friction coefficient shows a minimum, while for disparate proportions the friction coefficient grows. At the mushroom-to-brush transition (MBT) the viscosity scales with an exponent that depends on the characteristic exponent of the MBT (6/5) and the solvent quality exponent (ν=0.5, for θsolvent), but it is independent of the polymerization degree (N). On the other hand, the friction coefficient at the MBT scales as μ∼N^{6/5}, while the grafting density at the MBT scales as Γ∼N^{-6/5} when friction is minimal, in agreement with previous scaling theories. We argue these aspects are the result of cooperative phenomena that have important implications for the understanding of biological brushes and the design of microfluidics devices, among other applications of current academic and industrial interest.

Structural and thermodynamic consistency in coarse-grained models of macromolecules

Coarse-grained models of complex liquids are becoming increasingly important in simulations of complex fluids because they substantially reduce computational time while bridging information between simulations performed with atomistic resolution and continuum models. However, to be useful coarse-graining approaches need to provide physically consistent representations of the system under study, independent of the degree of coarse-graining resolution, i.e. they need to ensure consistency in both the thermodynamic and structural properties.Developing coarse-graining approaches that ensure consistency of thermodynamic and structural properties across variable coarse-graining resolution is a challenge. The difficulty is in properly mapping many-body interactions into effective pair interactions, which are input to the fast mesoscale molecular dynamic simulations of the coarse-grained representations.In this paper we review a Coarse-Grained approach, based on Integral Equation theory. This model conserves thermodynamics while accurately reproducing the structure of polymer liquids across variable levels of resolution. As it is solved analytically, it provides a formalism to reconstruct a posteriori the correct dynamics from the accelerated dynamics of the coarsegrained simulation. This approach has the advantage of being largely analytically solved and it is useful to highlight some important and general points that need to be considered when developing coarse-graining models.

Algorithms for GPU-based molecular dynamics simulations of complex fluids: Applications to water, mixtures, and liquid crystals.

A custom code for molecular dynamics simulations has been designed to run on CUDA-enabled NVIDIA graphics processing units (GPUs). The double-precision code simulates multicomponent fluids, with intramolecular and intermolecular forces, coarse-grained and atomistic models, holonomic constraints, Nosé-Hoover thermostats, and the generation of distribution functions. Algorithms to compute Lennard-Jones and Gay-Berne interactions, and the electrostatic force using Ewald summations, are discussed. A neighbor list is introduced to improve scaling with respect to system size. Three test systems are examined: SPC/E water; an n-hexane/2-propanol mixture; and a liquid crystal mesogen, 2-(4-butyloxyphenyl)-5-octyloxypyrimidine. Code performance is analyzed for each system. With one GPU, a 33-119 fold increase in performance is achieved compared with the serial code while the use of two GPUs leads to a 69-287 fold improvement and three GPUs yield a 101-377 fold speedup.

Parallelised Hoshen–Kopelman algorithm for lattice-Boltzmann simulations

We discuss two topics that we have encountered in our lattice-Boltzmann simulations of complex fluids: the sizes of droplets in particle-stabilised emulsions and deformable particles in fluid flow. The common factor in these seemingly disparate subjects is that both represent an opportunity for a novel application of the Hoshen–Kopelman algorithm. This algorithm is based on detecting connected clusters on a lattice and labelling the involved lattice sites such that all sites that are connected share the same label. The assumption of the presence of a lattice makes it a convenient algorithm to use in combination with lattice-Boltzmann simulations. In order to apply this algorithm on the fly during massively parallel simulations, it needs to be parallelised as well. We present our parallel implementation, which is tailored to a common parallelisation scheme for the lattice-Boltzmann method, and compare it to previous work. We then briefly discuss some examples of results obtained using this procedure.

A unified operator splitting approach for multi-scale fluid–particle coupling in the lattice Boltzmann method

A unified framework to derive discrete time-marching schemes for the coupling of immersed solid and elastic objects to the lattice Boltzmann method is presented. Based on operator splitting for the discrete Boltzmann equation, second-order time-accurate schemes for the immersed boundary method, viscous force coupling and external boundary force are derived. Furthermore, a modified formulation of the external boundary force is introduced that leads to a more accurate no-slip boundary condition. The derivation also reveals that the coupling methods can be cast into a unified form, and that the immersed boundary method can be interpreted as the limit of force coupling for vanishing particle mass. In practice, the ratio between fluid and particle mass determines the strength of the force transfer in the coupling. The integration schemes formally improve the accuracy of first-order algorithms that are commonly employed when coupling immersed objects to a lattice Boltzmann fluid. It is anticipated that they will also lead to superior long-time stability in simulations of complex fluids with multiple scales.

Complex fluid simulations with the parallel tree-based Lattice Boltzmann solver Musubi

We present the open source Lattice Boltzmann solver Musubi. It is part of the parallel simulation framework APES, which utilizes octrees to represent sparse meshes and provides tools from automatic mesh generation to post-processing. The octree mesh representation enables the handling of arbitrarily complex simulation domains, even on massively parallel systems. Local grid refinement is implemented by several interpolation schemes in Musubi. Various kernels provide different physical models based on stream-collide algorithms. These models can be computed concurrently and can be coupled with each other. This paper explains our approach to provide a flexible yet scalable simulation environment and elaborates its design principles and implementation details. The efficiency of our approach is demonstrated with a performance evaluation on two supercomputers and a comparison to the widely used Lattice Boltzmann solver Palabos.

Surface-based flow visualization

With increasing computing power, it is possible to process more complex fluid simulations. However, a gap between increasing data size and our ability to visualize them still remains. Despite the great amount of progress that has been made in the field of flow visualization over the last two decades, a number of challenges remain. While the visualization of 2D flow has many good solutions, the visualization of 3D flow still poses many problems. Challenges such as domain coverage, speed of computation, and perception remain key directions for further research. Flow visualization with a focus on surface-based techniques forms the basis of this literature survey, including surface construction techniques and visualization methods applied to surfaces. We detail our investigation into these algorithms with discussions of their applicability and their relative strengths and drawbacks. We review the most important challenges when considering such visualizations. The result is an up-to-date overview of the current state-of-the-art that highlights both solved and unsolved problems in this rapidly evolving branch of research.

S054011 MPCDを用いた複雑流体の数値シミュレーション

The behavior of star polymer in shear flow was investigated using Multi-Particle Collision Dynamics (MPCD),which is particle-based mesoscale hydrodynamic algorithm. MPCD is a suitable tool for the simulation of complex fluids because it can express both hydrodynamic interaction and Brownian motion, which are not negligible in the simulation of complex fluids. The present study considered the behavior of a star polymer under flow. A star polymer has many brunches interacting each other. In the present simulation a star polymer chain is consist of beads and elastic spring. The simulation was carried out by changing the number of brunches. The numerical results showed that the deformation behavior and conformation of star polymers depended on the number of branches.

Multiple time scale molecular dynamics for fluids with orientational degrees of freedom. II. Canonical and isokinetic ensembles

We have developed several multiple time stepping techniques to overcome the limitations on efficiency of molecular dynamics simulations of complex fluids. They include the modified canonical and isokinetic schemes, as well as the extended isokinetic Nosé-Hoover chain approach. The latter generalizes the method of Minary, Tuckerman, and Martyna for translational motion [Phys. Rev. Lett. 93, 150201 (2004)] to systems with both translational and orientational degrees of freedom. Although the microcanonical integrators are restricted to relatively small outer time steps of order of 16 fs, we show on the basis of molecular dynamics simulations of ambient water that in the canonical and isokinetic thermostats the size of these steps can be increased to 50 and 75 fs, respectively (at the same inner time step of 4 fs). Within the generalized isokinetic Nosé-Hoover chain algorithm we have derived, huge outer time steps of order of 500 fs can be used without losing numerical stability and affecting equilibrium properties.

Statistical Physics Problems in Adaptive Resolution Computer Simulations of Complex Fluids

Simulating complex fluids or in general complex molecular systems requires approaches covering decades of time and length scales. This usually cannot be achieved within one simulation model. Over the years many different methods and models have been developed ranging from rather generic models, representing most efficiently the universal statistical mechanical properties of e.g. polymers, to all atom models and even quantum mechanical treatments. While these allow for scientifically very important studies in their own right, only a combination and close link between models of different levels allows for a truly quantitative description of materials and processes. In the present contribution we discuss an adaptive resolution approach where different levels of detail are treated within one simulation and the molecules are free to diffuse between different regions in space, where the molecules interact with different interaction potentials.

Modern lattice Boltzmann methods for multiphase microflows

During the last decade, the Lattice Boltzmann (LB) method has captured an increasing attention as an efficient tool for the numerical simulation of complex fluids, particularly multi-phase and multi-component flows. In this paper, we revisit the basic features of two modern variants of lattice Boltzmann models for non-ideal fluids, which offer promising perspectives for the numerical simulation of complex micro-flows.

Over Two Decades of Integration‐Based, Geometric Flow Visualization

AbstractWith ever increasing computing power, it is possible to process ever more complex fluid simulations. However, a gap between data set sizes and our ability to visualize them remains. This is especially true for the field of flow visualization, which deals with large, time‐dependent, multivariate simulation data sets. In this paper, geometry‐based flow visualization techniques form the focus of discussion. Geometric flow visualization methods place discrete objects in the velocity field whose characteristics reflect the underlying properties of the flow. A great amount of progress has been made in this field over the last two decades. However, a number of challenges remain, including placement, speed of computation and perception. In this survey, we review and classify geometric flow visualization literature according to the most important challenges when considering such a visualization, a central theme being the seeding algorithm upon which they are based. This paper details our investigation into these techniques with discussions on their applicability and their relative merits and drawbacks. The result is an up‐to‐date overview of the current state‐of‐the‐art that highlights both solved and unsolved problems in this rapidly evolving branch of research. It also serves as a concise introduction to the field of flow visualization research.