Particle Solver Research Articles

A Lagrangian–Eulerian approach to modeling homogeneous condensation in high density gas expansions

A computational approach to homogeneous nucleation is proposed based on Eulerian description of the gas phase expansion coupled with a Lagrangian approach to the cluster formation. A continuum, Euler/Navier-Stokes solver versatile advection code is used to model the gas transport, and a kinetic particle solver is developed in this work to simulate cluster nucleation and growth. Parameters in the new model were adjusted so as to match the known theoretical dimer formation equilibrium constants for the two gases under consideration, argon and water. Reasonable agreement between computed and available experimental data was found in terminal cluster size distributions for nozzle water expansions in a wide range of stagnation pressures. The proposed approach was found to be orders of magnitude faster than a comparable approach based on the direct simulation Monte Carlo method.

Method of the Particle-in-Cell Simulation for the Y-Point in the Pulsar Magnetosphere

Abstract Recent observations in the X-ray and Gamma-ray suggest that the emission region of the pulsar magnetosphere can be multifold. In particular, the open-close boundary of the magnetic field, so-called the Y-point, can be a new candidate place where magnetic field energy converts into plasma heat and/or flow energy. Here, we present a new Particle-in-Cell code, which can be applied to the Y-point of the pulsar magnetosphere in axisymmetric geometry. The electromagnetic solver is used in two-dimensional grid points with cylindrical coordinates ($R$, $z$), while the particle solver operates in three-dimensional Cartesian coordinates ($x$, $y$, $z$), where the Buneman–Boris method is used. The particle motion is treated in special relativity. The inner boundary conditions are set up to generate rotation of the magnetosphere by use of the force-free semi-analytic solution given by Uzdensky (2003, ApJ, 598, 446). The code has been verified by dispersion relations of all wave modes in electron-positron plasmas. The initial test run is also presented to demonstrate the Y-shaped structure at the top of the dead zone on the light cylinder. We suggest that the structure is variable with quasi-periodicity with magnetic reconnection, and that plasma will be accelerated and/or heated. In a time-averaged point of view, the break up of the ideal-MHD (magneto-hydrodynamics) condition takes place in the vicinity of the Y-point.

A Hybrid Particle-Continuum Method for Hydrodynamics of Complex Fluids

A previously developed hybrid particle-continuum method [J. B. Bell, A. Garcia, and S. A. Williams, Multiscale Model. Simul., 6 (2008), pp. 1256–1280] is generalized to dense fluids and two- and three-dimensional flows. The scheme couples an explicit fluctuating compressible Navier–Stokes solver with the isotropic direct simulation Monte Carlo (DSMC) particle method [A. Donev, A. L. Garcia, and B. J. Alder, J. Stat. Mech. Theory Exp., 2009 (2009), article P11008]. To achieve bidirectional dynamic coupling between the particle (microscale) and continuum (macroscale) regions, the continuum solver provides state-based boundary conditions to the particle subdomain, while the particle solver provides flux-based boundary conditions for the continuum subdomain. This type of coupling ensures both state and flux continuity across the particle-continuum interface analogous to coupling approaches for deterministic parabolic partial differential equations; here, when fluctuations are included, a small ($<1\%$) mismat...

Adaptive time stepping for explicit euler implementation of spherical and non-spherical particle speed up

Numerical implementation schemes of drag force effects on Lagrangian particles can lead to instabilities or inefficiencies if static particle time stepping is used. Despite well known disadvantages, the programming structure of the underlying, C++ based, Lagrangian particle solver led to the choice of an explicit EULER, temporal discretization scheme. To optimize the functionality of the EULER scheme, this paper proposes a method of adaptive time stepping, which adjusts the particle sub time step to the need of the individual particle. A user definable adjustment between numerical stability and calculation efficiency is sought and a simple time stepping rule is presented. Furthermore a method to quantify numerical instability is devised and the importance of the characteristic particle relaxation time as numerical parameter is underlined. All derivations are being conducted for (non-)spherical particles and finally for a generalized drag force implementation. Important differences in spherical and non-spherical particle behaviour are pointed out.

A Duhamel approach for the Langevin equations with holonomic constraints

To simulate polymer flows in microscale environments we have developed a numerical method that couples stochastic particle dynamics with an efficient incompressible Navier–Stokes solver. Here, we examine properties of the particle solver alone. We derive a Duhamel-form stochastic particle method for freely jointed polymers and demonstrate that it achieves 2-order weak convergence and 3/2-order strong convergence with holonomic constraints. For time steps approaching the relaxation time, our method displays greatly enhanced stability relative to comparable solvers based on linearised dynamics. Under these same conditions, our method has solution errors that are approximately six orders of magnitude smaller than that for the linearised algorithm.

Study of the Flame-Burning Velocity Ratio Using PDF Monte Carlo Model

Various experimental and DNS data show that the interaction between turbulence and chemistry seriously affects the turbulent flame velocity ratio evolution. In this article, we have simulated turbulent premixed and stabilized flame growing in adiabatic combustion chamber in one-dimensional case. The turbulence is supposed to be isotropic and homogeneous. The chemistry is a single-stage scheme obeying Arrhenius law. The numerical simulation is based on the evolution PDF that uses Monte Carlo particle solver. We have emphasized on the turbulent flame-burning velocity ratio St/SL evolving versus respectively u′/SL and (u′/SL)Da 1/4. We have found that the flame-burning velocity shows a linear tendency in consent with Damköhler's limit model, Zimont-Liptanikov's model and with experimental data by Gülder et al. for moderate turbulence intensity. However, our simulation result shows a notable disagreement with some models as the one by Peters.

Modeling of plasma fibers with radiative processes

A fully three dimensional Particle in Cell model of the plasma flber had been developed. The code is written in FORTRAN 95, implementation CVF (Compaq Visual Fortran) under Microsoft Visual Studio user interface. Five particle solvers and two fleld solvers are included in the model. The solvers have relativistic and non{relativistic variants. The model can deal both with periodical and non{periodical boundary conditions. Plasma flber and its surroundings are generated during the initiation process. Many parameters of the flber, such as temperatures of electrons and ions, electric and magnetic flelds, perturbations in the shape of the flber and of the charged particle positions can be in∞uenced by the input dialog. The PIC program package simulates the behavior of the flber, namely the evolution of the magnetic fleld structures and turbulences. The numerical solution of the particle motion and calculation of the electric and magnetic flelds is the core of the program package. There are many additional routines and collaborating program packages for computer diagnostics, graphical output and other calculations such as radiation, collisions with neutrals, etc. The mechanism of the surface turbulences generation in the plasma flber was successfully simulated with the PIC program package. One of the latest goals of the PIC package was clariflcation of the onset of turbulence structures on the plasma flbers surfaces. It was shown that the development of these structures can be caused by initial a radial perturbation of plasma concentration and charge density. The surface structures simulated by PIC package were observed experimentally in various z{pinch apparatuses.

Multiphysics Modelling Environment for Continuum And Discrete Dynamics

A model-development environment for simulation of discrete and continuum dynamics in complex 3D geometries is described. This environment is based on 3D libraries for manipulation of geometrical primitives, object-oriented multidomain modelling paradigm, continuum solvers on unstructured meshes, discrete particle solvers, and a tool-assisted grid generation technique. The numerical approach is based on combined control-volume and finite-element methods of continuum mechanics and Lagrangian particle dynamics method. Several prototype example cases of complex continuum mechanical systems are considered, such as flow in bifurcating channels, including particle transport and deposition, flow interactions with flexible membranes and rigid structures, and a simplified model of molecular dynamics represented by a system of particles and bonds.

Multiphysics Modelling Environment for Continuum and Discrete Dynamics

AbstractA model-development environment for simulation of discrete and continuum dynamics in complex 3D geometries is described. This environment is based on 3D libraries for manipulation of geometrical primitives, object-oriented multidomain modelling paradigm, continuum solvers on unstructured meshes, discrete particle solvers, and a tool-assisted grid generation technique. The numerical approach is based on combined control-volume and finite-element methods of continuum mechanics and Lagrangian particle dynamics method. Several prototype example cases of complex continuum mechanical systems are considered, such as flow in bifurcating channels, including particle transport and deposition, flow interactions with flexible membranes and rigid structures, and a simplified model of molecular dynamics represented by a system of particles and bonds.

Particle and field solvers in PM models

A fully three-dimensional Particle Mesh model of the plasma fiber was developed in our department for numerical simulations of the onset of helical modes of the fiber. The tests of the particle and field solvers are described in this paper as well as results of the LIC (Line Integral Convolution) field visualization technique.

On a Finite-Element Method for Solving the Three-Dimensional Maxwell Equations

The aim of this paper is to present a method for solving the time-domain three-dimensional Maxwell equations, which can be coupled with a particle solver. For this purpose, Maxwell's equations are reformulated as a constrained wave equation system, with Lagrange multipliers associated to the conditions ∇ · β - 0 and ∇ · E - ρ/ε 0. We approximate both the fields and the Lagrange multipliers with a finite element method using a Taylor Hood element.