Gregg A. Radtke

Low-noise Monte Carlo simulation of the variable hard sphere gas

We present an efficient particle simulation method for the Boltzmann transport equation based on the low-variance deviational simulation Monte Carlo approach to the variable-hard-sphere gas. The proposed method exhibits drastically reduced statistical uncertainty for low-signal problems compared to standard particle methods such as the direct simulation Monte Carlo method. We show that by enforcing mass conservation, accurate simulations can be performed in the transition regime requiring as few as ten particles per cell, enabling efficient simulation of multidimensional problems at arbitrarily small deviation from equilibrium.

Lattice ellipsoidal statistical BGK model for thermal non- equilibrium flows

A thermal lattice Boltzmann model is constructed on the basis of the ellipsoidal statistical Bhatnagar-Gross-Krook (ES-BGK) collision operator via the Hermite moment representation. The resulting lattice ES-BGK model uses a single distribution function and features an adjustable Prandtl number. Numerical simulations show that using a moderate discrete velocity set, this model can accurately recover steady and transient solutions of the ES-BGK equation in the slip-flow and early transition regimes in the small Mach number limit that is typical of microscale problems of practical interest. In the transition regime in particular, comparisons with numerical solutions of the ES-BGK model, direct Monte Carlo and low-variance deviational Monte Carlo simulations show good accuracy for values of the Knudsen number up to approximately 0:5. On the other hand, highly non-equilibrium phenomena characterized by high Mach numbers, such as viscous heating and force-driven Poiseuille flow for large values of the driving force, are more difficult to capture quantitatively in the transition regime using discretizations that have been chosen with computational efficiency in mind such as the one used here, although improved accuracy is observed as the number of discrete velocities is increased.

On Variance-Reduced Simulations of the Boltzmann Transport Equation for Small-Scale Heat Transfer Applications

We present and discuss a variance-reduced stochastic particle simulation method for solving the relaxation-time model of the Boltzmann transport equation. The variance reduction, achieved by simulating only the deviation from equilibrium, results in a significant computational efficiency advantage compared with traditional stochastic particle methods in the limit of small deviation from equilibrium. More specifically, the proposed method can efficiently simulate arbitrarily small deviations from equilibrium at a computational cost that is independent of the deviation from equilibrium, which is in sharp contrast to traditional particle methods. The proposed method is developed and validated in the context of dilute gases; despite this, it is expected to directly extend to all fields (carriers) for which the relaxation-time approximation is applicable.

On efficient simulations of multiscale kinetic transport.

We discuss a new class of approaches for simulating multiscale kinetic problems, with particular emphasis on applications related to small-scale transport. These approaches are based on a decomposition of the kinetic description into an equilibrium part, which is described deterministically (analytically or numerically), and the remainder, which is described using a particle simulation method. We show that it is possible to derive evolution equations for the two parts from the governing kinetic equation, leading to a decomposition that is dynamically and automatically adaptive, and a multiscale method that seamlessly bridges the two descriptions without introducing any approximation. Our discussion pays particular attention to stochastic particle simulation methods that are typically used to simulate kinetic phenomena; in this context, these decomposition approaches can be thought of as control-variate variance-reduction formulations, with the nearby equilibrium serving as the control. Such formulations can provide substantial computational benefits in a broad spectrum of applications because a number of transport processes and phenomena of practical interest correspond to perturbations from nearby equilibrium distributions. In many cases, the computational cost reduction is sufficiently large to enable otherwise intractable simulations.

On the second-order temperature jump coefficient of a dilute gas

We use LVDSMC simulations to calculate the second-order temperature jump coecient for a dilute gas whose temperature is governed by the Poisson equation with a constant forcing term. Both the hard sphere gas and the BGK model of the Boltzmann equation are considered. Our results show that the temperature jump coecient is different from the well known linear and steady case where the temperature is governed by the homogeneous heat conduction (Laplace) equation.

Low Variance Particle Simulations of the Boltzmann Transport Equation for the Variable Hard Sphere Collision Model

We present and validate a variance reduced deviational particle method for simulating the Boltzmann transport equation for the variable hard sphere (VHS) collision operator. In comparison with the direct simulation Monte Carlo (DSMC) method, the proposed method is more suitable for simulating transport in regimes where the departure from equilibrium is small, such as dilute gas flows in small‐scale devices (MEMS, NEMS). In fact, the proposed method has a constant signal‐to‐noise ratio in the limit of small departure from equilibrium, and is thus able to simulate arbitrarily small deviations from equilibrium. The approach developed herein combines the variable hard sphere collision algorithm developed by Wagner [1] with an efficient advection routine based on Ref. [2]. The resulting method is stable and highly efficient, and results in dramatically reduced statistical noise in regimes typical of transport in small‐scale devices.

On Efficient Particle Methods for Solving the Boltzmann Transport Equation in the Relaxation-Time Approximation

We present and discuss a variance-reduced stochastic particle simulation method for solving the relaxation-time model of the Boltzmann transport equation. The variance reduction, achieved by simulating only the deviation from equilibrium, results in a significant computational efficiency advantage compared to traditional stochastic particle methods in the limit of small deviation from equilibrium. More specifically, the proposed method can efficiently simulate arbitrarily small deviations from equilibrium at a computational cost that is independent of the deviation from equilibrium, which is in sharp contrast to traditional particle methods. The proposed method is developed and validated in the context of dilute gases; despite this, it is expected to directly extend to all fields (carriers) for which the relaxation-time approximation is applicable.Copyright

The Response of a Gas in a Micro‐channel to Periodic Boundary Heating

We study the flow‐field generated in a one‐dimensional wall‐bounded gas layer due to periodic small‐amplitude time variation in the temperature of its boundaries. We focus on the Navier‐Stokes limit, where the layer width is large compared to the mean free path and the characteristic time‐scale of temperature variations is long compared with the mean free time between collisions. The viscous‐compressible Navier‐Stokes equations with slip‐flow boundary conditions are solved analytically for the case of sinusoidal heating. The analysis is then extended to study the system response to arbitrary periodic heating. Results are presented for both triangle‐ and square‐wave heating profiles. These solutions are found to be in good agreement with low‐variance Monte‐Carlo simulations of the Boltzmann equation, validating the present analysis as an accurate and simple alternative to expensive molecular computations. In addition, the analysis is applied for quantitative examination of the conditions for breakdown of t...

Effect of the Excess Volume of Lattice Defects on the Enthalpy of Formation and Desorption Temperature of Metal Hydrides

Metal and complex hydrides offer very promising prospects for hydrogen storage that reach the DOE targets for 2015. However, slow sorption kinetics and high release temperature must be addressed to make automotive applications feasible. Reducing the enthalpy of formation by destabilizing the hydride reduces the heat released during the hydrogenation phase and conversely allows desorption at a lower temperature. High-energy ball milling has been shown to decrease the release temperature, increase reaction kinetics and lower the enthalpy of formation in certain cases. Increased surface and grain boundary energy could play a role in reducing the enthalpy of formation, but the predicted magnitude is too small to account for experimental observations. As the particle and grain sizes are reduced considerably under high-energy treatments, structural defects and deformations are introduced. These regions can be characterized by an excess volume due to deformations in the lattice structure, and have a significant effect on the material properties of the hydride. We propose a thermodynamic model that characterizes the excess energy present in the deformed regions to explain the change in physical properties of metal hydrides. An experimental investigation using the TEM to study the effect of lattice deformations and other nanostructures on the desorption process is underway.Copyright