Hybrid atomistic-continuum simulation of nucleate boiling with domain re-decomposition method

The bubble nucleation plays a pivotal role in the boiling process. In order to have a comprehensive understanding of this phenomenon, a critical consideration on fluid-solid interaction at atomistic level is imperative. However, traditional Molecular Dynamics simulation requires prohibited amount of computational efforts to accomplish a full scale study. Hybrid atomistic-continuum method is a promising solution for this problem. It limits the atomistic region to a small scale where detailed information is preferable, while using continuum method for the rest of the domain. Nevertheless, none of the current hybrid method is suitable for solving a rapid expanding system like the bubble nucleation. In this study, a domain re-decomposition hybrid atomistic-continuum method is developed to conduct a multiscale/multiphase investigation on the bubble nucleation. In addition to the conventional coupling scheme, this method is capable to re-partition the molecular and continuum domain once it is necessary during the simulation. That is, the Computational Fluid Dynamics (CFD) and Molecular Dynamics (MD) regions are interchangeable on the fly such that the bubble is absolutely confined within MD region. Giving the fact that accurate modeling of interface tracking and phase change are still problematic for continuum mechanics on microscale, our coupling method directly avoids these issues since CFD domain takes care of a single-phase flow while the molecular domain simulates the bubble growth. With this idea in mind, this approach enables us to investigate the nucleate boiling on nanostructured surface with higher resolution than complete continuum mechanic model based simulation. In the present result, it is observed that bubble grows at a curved surface imposed with a constant super heat after nucleate boiling occurs. Meanwhile, the energy flux flows from solid to fluid is measured during the entire process. It is believed that this coupling method is very promising in studying nano-bubble related multiphase problems on microscale.

Coupling Strategies Investigation of Hybrid Atomistic-Continuum Method Based on State Variable Coupling

Different configurations of coupling strategies influence greatly the accuracy and convergence of the simulation results in the hybrid atomistic-continuum method. This study aims to quantitatively investigate this effect and offer the guidance on how to choose the proper configuration of coupling strategies in the hybrid atomistic-continuum method. We first propose a hybrid molecular dynamics- (MD-) continuum solver in LAMMPS and OpenFOAM that exchanges state variables between the atomistic region and the continuum region and evaluate different configurations of coupling strategies using the sudden start Couette flow, aiming to find the preferable configuration that delivers better accuracy and efficiency. The major findings are as follows:(1)theC→Aregion plays the most important role in the overlap region and the “4-layer-1” combination achieves the best precision with a fixed width of the overlap region;(2)the data exchanging operation only needs a few sampling points closer to the occasions of interactions and decreasing the coupling exchange operations can reduce the computational load with acceptable errors;(3)the nonperiodic boundary force model with a smoothing parameter of 0.1 and a finer parameter of 20 can not only achieve the minimum disturbance near the MD-continuum interface but also keep the simulation precision.

Finite-Temperature Quasi-Continuum

A generalization of the quasi-continuum (QC) method to finite temperature is presented. The resulting “hot-QC” formulation is a partitioned domain multiscale method in which atomistic regions modeled via molecular dynamics coexist with surrounding continuum regions. Hot-QC can be used to study equilibrium properties of systems under constant or quasistatic loading conditions. Two variants of the method are presented which differ in how continuum regions are evolved. In “hot-QC-static” the free energy of the continuum is minimized at each step as the atomistic region evolves dynamically. In “hot-QC-dynamic” both the atomistic and continuum regions evolve dynamically in tandem. The latter approach is computationally more efficient, but introduces an anomalous “mesh entropy” which must be corrected. Following a brief review of related finite-temperature methods, this review article provides the theoretical background for hot-QC (including new results), discusses the implementational details, and demonstrates the utility of the method via example test cases including nanoindentation at finite temperature.

About an analytical verification of quasi-continuum methods with Γ-convergence techniques

ABSTRACTQuasi-continuum (QC) methods are computational techniques, which reduce the complexity of atomistic simulations in a static setting while keeping information on small-scale structures and effects. The main idea is to couple atomistic and continuum models and thus to obtain quite detailed but still not too expensive numerical simulations.We aim at a mathematically rigorous verification of QC methods by means of discrete to continuum limits. In this article we present our first results for the so-called quasi-nonlocal QC method in the context of fracture mechanics. To this end we start from a one-dimensional chain of atoms with nearest and next-to-nearest neighbour interactions of Lennard-Jones type. This is considered as a fully atomistic model of which the Γ-limits (of zeroth and first order) for an infinite number of atoms are known [7].The QC models we construct are equal to this fully atomistic model in the atomistic region; in the continuum regime we approximate the next-to-nearest neighbour interactions by some nearest neighbour potential which is related to the so-called Cauchy-Born rule. Further we choose certain representative atoms in order to coarsen the mesh in the continuum region. It turns out that the selection of the representative atoms is crucial and influences the Γ-limits.We regard a QC model as good if the Γ-limits of zeroth and first order or at least their minimal values and minimizers are the same as those of the fully atomistic model. Our analysis shows that, while in an elastic regime only the size of the atomistic region matters, in the case of fracture a proper choice of the representative atoms is an essential ingredient.

Modeling and Simulation of Wave Propagation Based on Atomistic Field Theory

Motivated by the need for a more efficient simulation of material behavior at both larger length scale and longer time scale than direct molecular dynamics simulation, an atomistic field theory (AFT) for modeling and simulation of multiphase material systems has been developed. Atomistic formulation of the multiscale field theory and its corresponding finite element implementation are briefly introduced. By virtue of finite element analysis of classical continuum mechanics, we show the existing phenomena of spurious wave reflections at the interfaces between regions with different mesh sizes. AFT is employed to investigate the wave propagation in magnesium oxide from the atomistic region to the continuum region without any special numerical treatment. Unlike some other atomistic/continuum computational methods, AFT has demonstrated the capability to display both acoustic and optic types of wave motion. Numerical results show that AFT has the capability to significantly reduce the wave reflections at the interface. This work provides a more fundamental understanding of wave reflections at the atomistic/continuum interface.

A Concurrent Multiscale Method for Coupling Atomistic and Continuum Models at Finite Temperatures

A concurrent multi-scale modeling method for finite temperature simulation of solids is introduced. The objective is to represent far from equilibrium phenomena using an atomistic model and near equilibrium phenomena using a continuum model, the domain being partitioned in discrete and continuum regions, respectively. An interface sub-domain is defined between the two regions to provide proper coupling between the discrete and continuum models. While in the discrete region the thermal and mechanical processes are intrinsically coupled, in the continuum region they are treated separately. The interface region partitions the energy transferred from the discrete to the continuum into mechanical and thermal components by splitting the phonon spectrum into “low” and “high” frequency ranges. This is achieved by using the generalized Langevin equation as the equation of motion for atoms in the interface region. The threshold frequency is selected such to minimize energy transfer between the mechanical and thermal components. Mechanical coupling is performed by requiring the continuum degrees of freedom (nodes) to follow the averaged motion of the atoms. Thermal coupling is ensured by imposing a flux input to the atomistic region and using a temperature boundary condition for continuum. This makes possible a thermodynamically consistent, bi-directional coupling of the two models.

The Heterogeneous Multiscale Method for Dynamics of Solids with Applications to Brittle Cracks

We present a multiscale method for the modeling of dynamics of crystalline solids. The method employs the continuum elastodynamics model to introduce loading conditions and capture elastic waves, and near isolated defects, molecular dynamics (MD) model is used to resolve the local structure at the atomic scale. The coupling of the two models is achieved based on the framework of the heterogeneous multiscale method (HMM) and a consistent coupling condition with special treatment of the MD boundary condition. Application to the dynamics of a brittle crack under various loading conditions is presented. Elastic waves are observed to pass through the interface from atomistic region to the continuum region and reversely. Thresholds of strength and duration of shock waves to launch the crack opening are quantitatively studied and related to the inertia effect of crack tips.

Coupled Atomistic/Discrete Dislocation Simulations of Nanoindentation at Finite Temperature

Simulations of nanoindentation in single crystals are performed using a finite temperature coupled atomistic/continuum discrete dislocation (CADD) method. This computational method for multiscale modeling of plasticity has the ability of treating dislocations as either atomistic or continuum entities within a single computational framework. The finite-temperature approach here inserts a Nose-Hoover thermostat to control the instantaneous fluctuations of temperature inside the atomistic region during the indentation process. The method of thermostatting the atomistic region has a significant role on mitigating the reflected waves from the atomistic/continuum boundary and preventing the region beneath the indenter from overheating. The method captures, at the same time, the atomistic mechanisms and the long-range dislocation effects without the computational cost of full atomistic simulations. The effects of several process variables are investigated, including system temperature and rate of indentation. Results and the deformation mechanisms that occur during a series of indentation simulations are discussed.

Quasicontinuum Models for Interface Multiscale Model

A strategy of coupling length scales from atomistic to continuum is investigated on the basis of quasicontinuum model for interface fracture problems. In the model, an atomistic region of the interest is discretized by finite elements and the positions of atoms are prescribed by means of nodal displacements of the elements with shape function for the reduction of the degrees of freedom. Total energy of the system consists of interatomic potentials, and minimized through variational method employed in conventional finite element formulation. In this study, we deal with the fracture behavior of Cu-Fe interface crack in two dimensional problems, and investigate the adequate discretization manner around the crack tip in use of quasicontinuum method.