Lawrence Musson

An isochoric domain deformation method for computing steady free surface flows with conserved volumes

Abstract The domain deformation method has been applied successfully to steady state free surface flows where the volume of the flow domain is unknown [V.F. de Almeida, Gas–liquid counterflow through constricted passages, Ph.D. thesis, University of Minnesota, Minneapolis, MN 1995; P.A. Sackinger, P.R. Schunk, R.R. Rao, A Newton–Raphson pseudo-solid domain mapping technique for free and moving boundary problems: a finite element implementation, J. Comput. Phys. 125 (1996) 83–103; L.C. Musson, Two-layer slot coating, Ph.D. thesis, University of Minnesota, Minneapolis, MN 2001]; however, this method does not handle effectively problems where the volume of the flow domain is known a priori. This work extends the original domain deformation method to a new isochoric domain deformation method to account for the volume conservation. Like in the original domain deformation method, the unknown shape of the flow domain is mapped onto a reference domain by using the equations of an elastic pseudo-solid; the difference with the original method is that this pseudo-solid is considered incompressible. Because of the incompressibility, the pseudo-pressure of the mapping appears as a Lagrange multiplier in the equations, and it is determined only up to an arbitrary uniform datum. By analyzing the coupled fluid flow-mapping problem, we show that, in the finite-element setting, such pressure datum can be specified by replacing one continuity equation in the fluid domain.

Multiphase Reacting Flow Modeling of Singlet Oxygen Generators for Chemical Oxygen Iodine Lasers

Singlet oxygen generators are multiphase flow chemical reactors that produce energetic oxygen to be used as a fuel for chemical oxygen iodine lasers. In this paper, a theoretical model of the generator is presented that consists of a twophase reacting flow model that treats both the gas phase and dispersed (liquid droplet) phase. The model includes the discretization over droplet size distribution as well. Algorithms for the robust solution of the large set of coupled, nonlinear, partial differential equations enable the investigation of a wide range of operating conditions and even geometric design choices.

2D PIC-DSMC simulation of microscale breakdown after vacuum seal failure

Summary form only given. An electrostatic particle-in-cell code with complex boundary conditions and direct simulation Monte Carlo particle collisions performed on a separate, adaptable collision mesh is utilized to investigate DC breakdown after vacuum failure. Previously, it has been found that cold field electron emission can explain the breakdown voltage deviation from the Paschen curve measured for small gaps. Furthermore, prior 1D simulations found that breakdown was sensitive to a fixed non-uniform background neutral gas distribution across the gap and that if the gap size is of order the mean free path then gas concentrated near the anode results in smaller breakdown voltages because electrons reaching the anode have energies near the peak of the ionization cross section. In the present work the two electrodes are separated by a vacuum gap and air at atmospheric pressure is allowed to flow into the gap from either the anode or cathode due to a small “crack” in the electrode resulting in a non-uniform neutral gas distribution. The simulation includes Auger neutralization, cold field emission (CFE) of electrons, electron-neutral elastic, ionization, and excitation interactions and ion-neutral interactions including charge exchange. The simulated breakdown voltages at various electrode gap sizes are compared to the Paschen curve and breakdown is found to be sensitive to the neutral gas density distribution as it develops across the gap from either the cathode or anode leak.

PPPS-2013: Accommodating large temporal, spatial, and particle weighting demands for simulating vacuum ARC discharge

Summary form only given. We have developed novel modeling approaches for simulation breakdown of vacuum arcs. Initiating an arc in vacuum spans many orders of magnitude in temporal and spatial scales, and number densities. We have developed specific approaches for each of these challenges-some more tested than others. These approaches are implemented in Aleph, a massively parallel 3D unstructured mesh electrostatic PIC-DSMC code. Aleph includes dynamic load balancing, volume chemistry (elastic collisions, charge exchange, ionization, etc.), and a variety of surface mechanisms. Our tool chain allows us to use conformal meshes to CAD geometry, a requirement for production use.

Collisional sheath verification problem for PIC plasma models

Summary form only given. Exact solutions for the equations that predict the flow and state of plasmas are few and limited to very simple problems, and so computer aided solutions are important to study more interesting and complex plasmas. Verification problems are important for comparison with computed models to demonstrate that computational methods are implemented correctly. When exact solutions are unavailable, it is sometimes useful to benchmark against existing computed solutions. We present a comparison between our collisional kinetic plasma (PIC/DSMC) sheath model and a finite difference solution of a two-fluid collisional plasma sheath model1. Reasonable agreements in potential and density fields and wall current for collisionless to weakly-collisional sheaths between the two models are obtained. A stochastic Richardson Extrapolation technique is used to obtain convergence rates, the extrapolated computational solution and 95% confidence intervals.

1D PIC simulation of microscale breakdown in gaps with a non-uniform background neutral gas density

Summary form only given. An explicit, electrostatic particle-in-cell (PIC) code with complex boundary conditions and direct simulation Monte Carlo (DSMC) particle collisions is utilized to investigate one dimensional direct current breakdown. Two electrodes are separated by a microscale gap with a non-uniform neutral gas distribution. For example, there may be a higher density near the anode as a result of vacuum seal failure near the anode. The simulation model includes Auger neutralization and cold field electron emission from the cathode as well as electron-neutral elastic, ionization, and excitation interactions. The simulated breakdown voltages at various electrode gap sizes are compared to experimental data and the Paschen curve. Previously, it has been found that cold field electron emission can explain the breakdown voltage deviation from the Paschen curve measured for small gaps. Furthermore, even in large gaps, as breakdown proceeds the plasma density becomes large enough and thus the cathode sheath thin enough that cold field emission dominates and super-exponential current growth results. Breakdown was found to be sensitive to the neutral gas density distribution across the gap. Specifically, if the gap is large enough that the cold field emission is negligible then gas concentrated near the cathode results in higher breakdown voltages since electrons leaving the cathode due to Auger neutralization are not yet energetic enough to ionize the high density neutral gas at the cathode. Conversely, if the gap size is of order the mean free path then gas concentrated near the anode results in smaller breakdown voltages because the electrons reaching the anode have energies near the peak of the ionization cross section near the higher density anode region. These lower breakdown voltages should be taken into account when designing vacuum electronics for failure tolerance.

Solution comparisons of models of an expanding ambipolar plasma

A common phenomenon in plasma transport is ambipolar expansion; the ambipolar expansion rate is the typical rate at which a neutral plasma will expand into a vacuum. This expansion is particularly important, for example, in understanding how quickly a plasma will fill a gap in high power electronics or in understanding how energy is transported in intense laser-driven plasmas. Often times, a plasma simulation must accurately capture the ambipolar expansion of a neutral plasma. We present simulation benchmarks for three codes: one plasma fluid code1 and two kinetic plasma codes - one of the kinetic codes using an unstructured mesh and the other a structured mesh. We compare results from these codes to analytic models and previously published simulation results. We discuss speed and accuracy for these three different approaches, specifically including a discussion of particle splitting and combining algorithms in the kinetic approaches.

3D vacuum ARC breakdown simulation: Many challenges and some solutions

Summary form only given. We present our current capabilities and plans targeting the simulation of 3D vacuum arc discharge in realistic geometries. Vacuum arc discharge is an incredibly challenging problem due to the enormous dynamic changes in plasma growth, collisional processes, and time scales. Our simulation model targets a co-planar Cu-Cu vacuum breakdown experiment. We will estimate the computational requirements for this physically relevant breakdown system assuming a fully kinetic description. A fully kinetic description is required to accurately capture the initial breakdown. Progress on unstructured mesh collisional PIC methodology, dynamic particle weighting, managing multiple temporal and spatial scales, electrode models, and efficient parallel scaling will be addressed.

ChISELS 1.0: theory and user manual :a theoretical modeler of deposition and etch processes in microsystems fabrication.

Chemically Induced Surface Evolution with Level-Sets--ChISELS--is a parallel code for modeling 2D and 3D material depositions and etches at feature scales on patterned wafers at low pressures. Designed for efficient use on a variety of computer architectures ranging from single-processor workstations to advanced massively parallel computers running MPI, ChISELS is a platform on which to build and improve upon previous feature-scale modeling tools while taking advantage of the most recent advances in load balancing and scalable solution algorithms. Evolving interfaces are represented using the level-set method and the evolution equations time integrated using a Semi-Lagrangian approach [1]. The computational meshes used are quad-trees (2D) and oct-trees (3D), constructed such that grid refinement is localized to regions near the surface interfaces. As the interface evolves, the mesh is dynamically reconstructed as needed for the grid to remain fine only around the interface. For parallel computation, a domain decomposition scheme with dynamic load balancing is used to distribute the computational work across processors. A ballistic transport model is employed to solve for the fluxes incident on each of the surface elements. Surface chemistry is computed by either coupling to the CHEMKIN software [2] or by providing user defined subroutines. This report describes the theoretical underpinnings, methods, and practical use instruction of the ChISELS 1.0 computer code.