Many-particle charged-particle plasma simulations using spatial meshes for the electromagnetic field solutions, particle-in-cell (PIC) merged with Monte Carlo collision (MCC) calculations, are coming into wide use for application to partially ionized gases. The author emphasizes the development of PIC computer experiments since the 1950s starting with one-dimensional (1-D) charged-sheet models, the addition of the mesh, and fast direct Poisson equation solvers for 2-D and 3-D. Details are provided for adding the collisions between the charged particles and neutral atoms. The result is many-particle simulations with many of the features met in low-temperature collision plasmas; for example, with applications to plasma-assisted materials processing, but also related to warmer plasmas at the edges of magnetized fusion plasmas. >

Particle-in-Cell Charged Particle Simulations, plus Monte Carlo Collisions with Neutral Atoms, PIC-MCC

▪ Abstract The principles of and procedures for implementing direct simulation Monte Carlo (DSMC) are described. Guidelines to inherent and external errors common in DSMC applications are provided. Three applications of DSMC to transitional and nonequilibrium flows are considered: rarefied atmospheric flows, growth of thin films, and microsystems. Selected new, potentially important advances in DSMC capabilities are described: Lagrangian DSMC, optimization on parallel computers, and hybrid algorithms for computations in mixed flow regimes. Finally, the limitations of current computer technology for using DSMC to compute low-speed, high–Knudsen-number flows are outlined as future challenges.

Direct Simulation Monte Carlo: Recent Advances and Applications

A Guide to Monte Carlo Simulations in Statistical Physics: Reweighting methods

ion reactions by primary radicals, for example: C6H5Cl + •Cl f C6H4Cl• + HCl ∆H°rxn ) from -109.3 to -66.4 kJ/mol Radical-radical recombination reactions, for example: Cl• + •Cl f Cl2 ∆H°rxn ) -239.2 kJ/mol C6H5• + •C6H5 f C12H10 ∆H°rxn ) -564.4 to -478.9 kJ/mol Computer Simulations of Laser Ablation of Molecular Substrates Chemical Reviews, 2003, Vol. 103, No. 2 327

Computer Simulations of Laser Ablation of Molecular Substrates

New developments are presented in the area of grid convergence error analysis and error estimation for mixed-order numerical schemes. A mixed-order scheme is defined here as a numerical method where the order of the local truncation error varies either spatially (e.g., at a shock wave) or for different terms in the governing equations (e.g., first-order convection with second-order diffusion). The case examined herein is the Mach 8 laminar flow of a perfect gas over a sphere-cone geometry. This flowfield contains a strong bow shock wave where the formally second-order numerical scheme is reduced to first order via a flux limiting procedure. The mixedorder error analysis method allows for non-monotone behavior in the solutions variables as the mesh is refined. Non-monotonicity in the local solution variables is shown to arise from a cancellation of first- and second-order error terms for the present case. The proposed error estimator, which is based on the mixed-order analysis, is shown to provide good estimates of the actual error. Furthermore, this error estimator nearly always provides conservative error estimates, in the sense that the actual error is less than the error estimate, for the case examined.

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Grid Convergence Error Analysis for Mixed-Order Numerical Schemes

We review the state of modeling and simulation of nuclear fuels with emphasis on the most widely used nuclear fuel, UO2. The hierarchical scheme presented represents a science-based approach to modeling nuclear fuels by progressively passing information in several stages from electronic structure calculations to continuum level simulations. Such an approach is essential to overcome the challenges posed by radioactive materials handling, experimental limitations in modeling extreme conditions and accident scenarios, and the small time and distance scales of fundamental processes. When used in conjunction with experimental validation, this multiscale modeling scheme can provide valuable guidance to development of fuel for advanced reactors to meet rising global energy demand.

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Modeling and simulation of nuclear fuel materials

We present a two dimensional direct simulation Monte Carlo (DSMC) study of the rarefied reactive flow of neutrals and ions in a low pressure inductively coupled plasma reactor. The spatially-dependent rate coefficients of electron impact reactions and the electrostatic field were obtained from a fluid plasma simulation. Neutral and ion etching of polysilicon with chlorine gas was studied with emphasis on the reaction uniformity along the wafer. Substantial gradients in total gas density were observed across the reactor invalidating the commonly made assumption of constant gas density. The flow was nonequilibrium with differences in the species translational temperatures, and 100 K temperature jumps near the walls. When etching was limited by ions the etch rate was highest at the wafer center. When etching was limited by neutrals, the etch rate was highest at the wafer edge. In such case, the etch uniformity changed significantly depending on the reactivity of the ring surrounding the wafer. The ion angular distribution was several degrees off normal and it was different at the wafer edge compared to the rest of the wafer. >

Two-dimensional direct simulation Monte Carlo (DSMC) of reactive neutral and ion flow in a high density plasma reactor

Icarus is a 2D Direct Simulation Monte Carlo (DSMC) code which has been optimized for the parallel computing environment. The code is based on the DSMC method of Bird[11.1] and models from free-molecular to continuum flowfields in either cartesian (x, y) or axisymmetric (z, r) coordinates. Computational particles, representing a given number of molecules or atoms, are tracked as they have collisions with other particles or surfaces. Multiple species, internal energy modes (rotation and vibration), chemistry, and ion transport are modeled. A new trace species methodology for collisions and chemistry is used to obtain statistics for small species concentrations. Gas phase chemistry is modeled using steric factors derived from Arrhenius reaction rates or in a manner similar to continuum modeling. Surface chemistry is modeled with surface reaction probabilities; an optional site density, energy dependent, coverage model is included. Electrons are modeled by either a local charge neutrality assumption or as discrete simulational particles. Ion chemistry is modeled with electron impact chemistry rates and charge exchange reactions. Coulomb collision cross-sections are used instead of Variable Hard Sphere values for ion-ion interactions. The electro-static fields can either be: externally input, a Langmuir-Tonks model or from a Green's Function (Boundary Element) based Poison Solver. Icarus has been used for subsonic to hypersonic, chemically reacting, and plasma flows. The Icarus software package includes the grid generation, parallel processor decomposition, post-processing, and restart software. The commercial graphics package, Tecplot, is used for graphics display. All of the software packages are written in standard Fortran.

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Icarus: A 2-D Direct Simulation Monte Carlo (DSMC) Code for Multi-Processor Computers

Direct Simulation Monte Carlo (DSMC) and NavierStokes calculations are performed for a Mach 11 25 deg.-55 deg. spherically blunted biconic. The conditions are such that flow is laminar, with separation occurring at the cone-cone juncture. The simulations account for thermochemical nonequilibrium based on standard Arrhenius chemical rates for nitrogen dissociation and Millikan and White vibrational relaxation. The simulation error for the Navier-Stokes (NS) code is estimated to be 2% for the surface pressure and 10% for the surface heat flux. The grid spacing for the DSMC simulations was adjusted to be less than the local mean-freepath (mfp) and the time step less than the cell transient time of a computational particle. There was overall good agreement between the two simulations; however, the recirculation zone was computed to be larger for the NS simulation. A sensitivity study is performed to examine the effects of experimental uncertainty in the freestream properties on the surface pressure and heat flux distributions. The surface quantities are found to be extremely sensitive to the vibrational excitation state of the gas at the test section, with differences of 25% found in the surface pressure and 25%-35% for the surface heat flux. These calculations are part of a blind validation comparison and thus the experimental data has not yet been re

/pdf/dsmc-and-navier-stokes-predictions-for-hypersonic-laminar-45frfg4pa6.pdf

Timothy Bartel

Papers

Modeling and simulation of nuclear fuel materials

Two-dimensional direct simulation Monte Carlo (DSMC) of reactive neutral and ion flow in a high density plasma reactor

Icarus: A 2-D Direct Simulation Monte Carlo (DSMC) Code for Multi-Processor Computers

DSMC and Navier-Stokes Predictions for Hypersonic Laminar Interacting Flows

DSMC simulation of nozzle expansion flow fields