Witold Alda

CROSS-SCALE NUMERICAL SIMULATIONS USING DISCRETE PARTICLE MODELS

Abstract We propose a concept for a homogenous computational model in carrying out cross-scale numerical experiments on liquids. The model employs the particle paradigm and comprises three types of simulation techniques: molecular dynamics (MD), dissipative particle dynamics (DPD) and smoothed particle hydrodynamics (SPH). With respect to the definition of the collision operator, this model may work in different hierarchical spatial and time scales as: MD in the atomistic scale, DPD in the mesoscale and SPH in the macroscale. The optimal computational efficiency of the three types of cross-scale experiments are estimated in dependence on: the system size N-where N is the number of particles-and the number of processors P employed for computer simulation. For the three-hierarchical-stage, as embodied in the MD-DPD-SPH model, the efficiency is proportional to N 8/7 but its dependence on P is different for each of the three types of cross-scale experiments. The problem of matching the different scales is dis...

Turbulent mixing in the microscale: a 2D molecular dynamics simulation

Results of 2D molecular dynamics (MD) method are presented for the mixing phenomenon in the microscale, where the length and time are measured in terms of microns and nanoseconds, respectively. Particle ensembles consisting of 0.7‐3 10 6 particles in 1.3‐510 5 timesteps were simulated. We focus on the temporal evolution of mixing layer between two superimposed Lennard‐Jones particle systems in a gravitational field directed from the heavier to the lighter particle fluid, and compare its properties with those observed in the macroworld. It is shown that the bubble-and-spikes stage of mixing process is similar in both the molecular scale and in the macroworld. The mixing layer growth constant A, which can be estimated using MD, is approximately the same as that obtained for 2D simulations in the macroscale, where the Navier‐Stokes equations are used. For the closed particle systems, we show that the value A remains stable for changing physical conditions, as it is in the macroscale. For the open particle systems with a free surface A is 20% higher and reaches the value 0.07, i.e., the same as that obtained in laboratory experiments. The influence of fluid granularity on the speed of mixing can be observed at a very early stage. This start-up time is connected with spontaneous instabilities formation, which appears as the cumulative result of thermal fluctuations. The occurrence of Rayleigh‐Taylor instability in the microscale, and its similarity to the same process in the macroscale, can also expand the scope of the term “turbulence” to microscaled flows on the molecular scale. ©2000 Elsevier Science B.V. All rights reserved.

Using Discrete Particles As a Natural Solver In Simulating Multiple-Scale Phenomena

Abstract We propose here the usage of different discrete particle methods for simulating both mesoscopic and macroscopic phenomena with hierarchical structures. Results of large-scale MD simulations of the Rayleigh-Taylor instability are shown and discussed. Using about one million Lennard-Jones particles, we have simulated particle fluid environments with a length scale of about 0.5 μm. For encompassing greater length and time scales, either more complex particle method or simplified MD model must be used. In the first case, we study dissipative particle dynamics (DPD) in modeling complex multi-component fluids flows, e.g., bubble formation, fluid flows in porous media, mixing driven by sedimentation. We also demonstrate how the particle method can be utilized for simulating a flexible surface with multiple scales present. We emphasize that the inherent parallelism of the MD method makes this approach a powerful natural solver of a wide variety of physical phenomena with multiple scales.

Complex fluid-dynamical phenomena modeled by large-scale molecular-dynamics simulations

We carried out large-scale molecular-dynamics simulations of the classical Rayleigh–Taylor (RT) phenomenon in a Lennard-Jones molecular liquid. We have observed from these simulations, involving 106–107 particles, the development of hydrodynamic instabilities from two different kinds of interacting particles. A free surface is introduced by deploying an overlying void. For a box with a dimension up to about 1 μm and two layers having different particle sizes, the fingering type of instability is observed as a result of oscillations caused by the gravitational field. In this gridless scheme, surface waves can be captured self-consistently. For equally sized particles, a spontaneous “fluctuation driven” mixing with a long start-up time is observed. These molecular- dynamics results suggest the possibilities of upscaling the RT phenomenon. For conducting these numerical experiments, which require at least ∼105 time steps, a single simulation would require 100–200 Tflops of massively parallel computer power. ...

Macro-Scale Simulations Using Molecular Dynamics Method

Abstract In this paper a new approach to the simulation of shock phenomena is presented. The discrete model of matter description is applied. The system representing a physical object consists of a large number of mutually interacting “particles” (N ∼ 105 +). The model can be used as an alternative to the model of continuous medium described by the sets of partial differential equations solved numerically, using for example the finite elements method. For the presented method, the time evolution of the particle system is described by the Newtonian laws of motion. Application of this approach for simulation of stress and shock phenomena is discussed. The results of selected simulations of the penetration mechanics, explosion and squashing are presented.

An examination of long-rod penetration in micro-scale using particles

Abstract The authors show how using particle simulations one can try to solve the problems out of reach of classical models based on the matter, momenta and energy flows continuity. Being aware about limitations of the method applied, the paper presents the perspectives of particle based simulations considering as an example the penetration mechanism investigation in micro-scale.

The results and perspectives of the particles method approach in investigations of plastic deformations I. Penetration mechanism

Abstract In the paper the assumptions of the particles method are presented and adapted to macroscopic quasi-particles and quasi-potentials. The system representing a physical object consists of a large number of mutually interacting “particles” ( N ≈ 10 5 +). The model can be used as an alternative to the model of continuous medium described by the set of partial differential equations, usually solved by the finite elements method (FEM). The advantages and disadvantages of both approaches for the simulation of shocking phenomena are discussed. The unique character of the presented method for simulation of non-continuities of the matter under stress is exemplified by the preliminary results obtained for simulation of projectile and long rod penetration.

Molecular Simulation of Mixing Fluids and Microhydrodynamic Instabilities

In the paper we report some results of simulation of instabilities accompanying the process of mixing two fluids with and without sedimentation. Molecular dynamics approach was used to investigate systems composed of 2·105 particles. To perform sufficiently long runs, we have been obliged to use efficient codes on parallel and vector architectures.

New Sky Pattern Recognition Algorithm

We present here a new algorithm which enables the identification of stars in astronomical photographs using readily available star catalogs for this purpose. The algorithm was implemented in a stand-alone application called `Skyprint` capable of performing a matching process. The computational aspect of the problem can be designated to the wide class of image recognition methods and analysis of multidimensional data. The astronomical aspect concentrates on astrometry --- the method of determining the coordinates of stars in the celestial sphere. The problem of identifying star patterns occurs most often in such areas as cosmic probe navigation, adjusting and merging numerous photographs of the sky together, or in recovering missing information in relation to a fragment of the sky represented in the photograph.

Family of Energy Conserving Glossy Reflection Models

We present an improved reflection model optimized for global illumination. The model produces visually plausible images, is symmetric and has improved energy preserving capabilities compared to previous approaches which satisfies these requirements. Having an efficient sampling routine, the model is ready to use in Monte Carlo rendering. Presented model is phenomenological, i.e. it has intuitive glossiness parameter that affects its appearance. Moreover it can be used as a set of basis functions designed to fit material reflection to measured data.