132 research outputs found
An alternative approach to efficient simulation of micro/nanoscale phonon transport
Starting from the recently proposed energy-based deviational formulation for
solving the Boltzmann equation [J.-P. Peraud and N. G. Hadjiconstantinou, Phys.
Rev. B 84, 2011], which provides significant computational speedup compared to
standard Monte Carlo methods for small deviations from equilibrium, we show
that additional computational benefits are possible in the limit that the
governing equation can be linearized. The proposed method exploits the
observation that under linearized conditions (small temperature differences)
the trajectories of individual deviational particles can be decoupled and thus
simulated independently; this leads to a particularly simple and efficient
algorithm for simulating steady and transient problems in arbitrary
three-dimensional geometries, without introducing any additional approximation.Comment: 4 pages, 2 figure
Solving the Boltzmann Equation on GPU
We show how to accelerate the direct solution of the Boltzmann equation using
Graphics Processing Units (GPUs). In order to fully exploit the computational
power of the GPU, we choose a method of solution which combines a finite
difference discretization of the free-streaming term with a Monte Carlo
evaluation of the collision integral. The efficiency of the code is
demonstrated by solving the two-dimensional driven cavity flow. Computational
results show that it is possible to cut down the computing time of the
sequential code of two order of magnitudes. This makes the proposed method of
solution a viable alternative to particle simulations for studying unsteady low
Mach number flows.Comment: 18 pages, 3 pseudo-codes, 6 figures, 1 tabl
Adjoint-based deviational Monte Carlo methods for phonon transport calculations
In the field of linear transport, adjoint formulations exploit linearity to derive powerful reciprocity relations between a variety of quantities of interest. In this paper, we develop an adjoint formulation of the linearized Boltzmann transport equation for phonon transport. We use this formulation for accelerating deviational Monte Carlo simulations of complex, multiscale problems. Benefits include significant computational savings via direct variance reduction, or by enabling formulations which allow more efficient use of computational resources, such as formulations which provide high resolution in a particular phase-space dimension (e.g., spectral). We show that the proposed adjoint-based methods are particularly well suited to problems involving a wide range of length scales (e.g., nanometers to hundreds of microns) and lead to computational methods that can calculate quantities of interest with a cost that is independent of the system characteristic length scale, thus removing the traditional stiffness of kinetic descriptions. Applications to problems of current interest, such as simulation of transient thermoreflectance experiments or spectrally resolved calculation of the effective thermal conductivity of nanostructured materials, are presented and discussed in detail.United States. Dept. of Energy. Office of Science (Solid-State Solar-Thermal Energy Conversion Center Award DE-FG02-09ER46577)United States. Dept. of Energy. Office of Science (Solid-State Solar-Thermal Energy Conversion Center Award DE-SC0001299
Low-Variance Monte Carlo Simulation of Thermal Transport in Graphene
ue to its unique thermal properties, graphene has generated considerable interest in the context of thermal management applications. In order to correctly treat heat transfer in this material, while still reaching device-level length and time scales, a kinetic description, such as the Boltzmann transport equation, is typically required. We present a Monte Carlo method for obtaining numerical solutions of this description that dramatically outperforms traditional Monte Carlo approaches by simulating only the deviation from equilibrium. We validate the simulation method using an analytical solution of the Boltzmann equation for long graphene nanoribbons; we also use this result to characterize the error associated with previous approximate solutions of this problem.National Science Foundation (U.S.). Graduate Research Fellowship ProgramAmerican Society for Engineering Education. National Defense Science and Engineering Graduate FellowshipSingapore-MIT Allianc
Efficient simulation of multidimensional phonon transport using energy-based variance-reduced Monte Carlo formulations
We present a new Monte Carlo method for obtaining solutions of the Boltzmann
equation for describing phonon transport in micro and nanoscale devices. The
proposed method can resolve arbitrarily small signals (e.g. temperature
differences) at small constant cost and thus represents a considerable
improvement compared to traditional Monte Carlo methods whose cost increases
quadratically with decreasing signal. This is achieved via a control-variate
variance reduction formulation in which the stochastic particle description
only solves for the deviation from a nearby equilibrium, while the latter is
described analytically. We also show that simulating an energy-based Boltzmann
equation results in an algorithm that lends itself naturally to exact energy
conservation thereby considerably improving the simulation fidelity.
Simulations using the proposed method are used to investigate the effect of
porosity on the effective thermal conductivity of silicon. We also present
simulations of a recently developed thermal conductivity spectroscopy process.
The latter simulations demonstrate how the computational gains introduced by
the proposed method enable the simulation of otherwise intractable multiscale
phenomena
Some properties of the kinetic equation for electron transport in semiconductors
The paper studies the kinetic equation for electron transport in semiconductors. New formulas for the heat generation rate are derived by analyzing the basic scattering mechanisms. In addition, properties of the steady state distribution are discussed and possible extensions of the deviational particle Monte Carlo method to the area of electron transport are proposed
A direct method for the Boltzmann equation based on a pseudo-spectral velocity space discretization
A deterministic method is proposed for solving the Boltzmann equation. The
method employs a Galerkin discretization of the velocity space and adopts, as
trial and test functions, the collocation basis functions based on weights and
roots of a Gauss-Hermite quadrature. This is defined by means of half- and/or
full-range Hermite polynomials depending whether or not the distribution
function presents a discontinuity in the velocity space. The resulting
semi-discrete Boltzmann equation is in the form of a system of hyperbolic
partial differential equations whose solution can be obtained by standard
numerical approaches. The spectral rate of convergence of the results in the
velocity space is shown by solving the spatially uniform homogeneous relaxation
to equilibrium of Maxwell molecules. As an application, the two-dimensional
cavity flow of a gas composed by hard-sphere molecules is studied for different
Knudsen and Mach numbers. Although computationally demanding, the proposed
method turns out to be an effective tool for studying low-speed slightly
rarefied gas flows
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