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Showing 1 to 20 of 99 for “"Boltzmann Equation"”.
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Reduced basis method for Boltzmann equation
… solve the BGK model of the Knudsen parameterized Boltzmann equation which is 1-d with respect to both space and velocity. In order to solve the Boltzmann equation, we first transform the original differential equation by replacing the dependent variable with another variable, weighted with …
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Analysis of the generalized Boltzmann equation.
Thesis: M.S., Massachusetts Institute of Technology, Department of Nuclear Engineering, 1972
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Some Problems Connected with the Boltzmann Equation
<p>Consider a dilute gas composed of a very large number of molecules moving in space according to the laws of classical mechanics, and colliding in pairs from time to time. Assume that we can disregard all external effects, such as gravity, so that the motion is completely specified by giving the …
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Multilevel Methods for the Poisson-Boltzmann Equation
We consider the numerical solution of the Poisson-Boltzmann equation (PBE), a three-dimensional second order nonlinear elliptic partial differential equation arising in biophysics. This problem has several interesting features impacting numerical algorithms, including discontinuous coefficients …
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QCD Boltzmann equation: beyond the soft-scattering approximation
… equilibrium. To that end, we investigate the QCD Boltzmann equation making use of a calculation scheme that reproduces the known result for scalar interactions and generalizes to a QCD interaction, under an approximation of soft scattering.
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Efficient particle methods for solving the Boltzmann equation
A new particle simulation method for solving the Boltzmann equation is presented and tested. This method holds a significant computational efficiency advantage for low-signal flows compared to traditional particle methods such as the Direct Simulation Monte Carlo (DSMC). More specifically, the …
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A Numerical Solution of Low-Energy Neutron Boltzmann Equation
<p>A multigroup method using a straight ahead approximation is created to calculate low energy neutron fluence due to the elastic scattering of evaporation neutrons produced in interactions of high energy particles with target nuclei. This multigroup method is added to NASA Langley Research …
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Boltzmann equation studies of the off-equilibrium QCD phenomena
… the partons to be on-shell is the relativistic Boltzmann equation. We develop parallel code to solve the relativistic Boltzmann equation in the relaxation time approximation in 3 + 1 dimensions (without simplifying assumptions on possible symmetries of the dynamics). Our approach, solving for …
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On the Boltzmann equation, quantitative studies and hydrodynamical limits
… kinetic theory and focuses more precisely on the Boltzmann equation. We investigate several properties of the solutions to the latter equation: their positivity and their hydrodynamical limits for instance. We also study the local Cauchy problem for a quantic version of the Boltzmann equation.
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Runge-Kutta Discontinuous Galerkin method for the Boltzmann equation
… provide accurate and efficient solutions of the Boltzmann equation. Solutions of the Boltzmann equation are desirable in connection to small scale science and technology because when characteristic flow length scales become of the order of, or smaller than, the molecular mean free path, the …
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Three Methods for Solving the Low Energy Neutron Boltzmann Equation
<p>The solution to the neutron Boltzmann equation is separated into a straightahead component dominating at high energies and an isotropic component dominating at low energies. The high-energy solution is calculated using HZETRN-05, and the low-energy isotropic component is modeled by two …
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Kac's process and some probabilistic aspects of the Boltzmann equation
… corresponding to the spatially homogeneous Boltzmann equation. We consider Kac's problem of showing propagation of chaos - that if the velocities of the particles are initially approximately independent, then the same is true at later times - which is equivalent to the convergence of the …
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Full 3+1 dimensional simulation of the relativistic Boltzmann equation
… An alternative to hydrodynamics is solving the Boltzmann equation, which describes the evolution of the full distribution function of the system without the close to equilibrium requirement. Large scale simulations using the Boltzmann equation, however, has hitherto proved computationally …
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Discontinuous Galerkin solution of the Boltzmann equation in multiple spatial dimensions
… alternative solution techniques for the Boltzmann equation typically used when the Knudsen number (ratio of molecular mean free path to characteristic length scale of flow) exceeds (approximately) 0.1. Alternative solution methods are required because the prevalent Boltzmann solution …
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A Forward-Backward Fluence Model for the Low-Energy Neutron Boltzmann Equation
<p>In this research work, the neutron Boltzmann equation was separated into two coupled integro-differential equations describing forward and backward neutron fluence in selected materials. Linear B-splines were used to change the integro-differential equations into a coupled system of ordinary …
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Shock phenomena for the one-dimensional Boltzmann equation and related kinetic problems
… sixth problem, on the justification of continuum equations from atomistic interactions. In particular, we focus on approximations of two-dimensional incompressible flow by finitely many interacting point vortices. Additionally, we study approximations of compressible gas dynamics by the Boltzmann …
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An excursion with the Boltzmann equation at low speeds : variance-reduced DSMC
… they are typically described using the Boltzmann equation which is most efficiently solved using a stochastic particle simulation method known as direct simulation Monte Carlo (DSMC). The latter is a simple and versatile simulation method which is very efficient in producing samples of …
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Efficient numerical methods for solving the Boltzmann equation for low-speed flows
… larger than approximately 0.1, the Navier-Stokes equations are no longer valid. In this case, which is frequently encountered in small-scale flows, one must solve the more general Boltzmann equation. The objective of this work is to develop a method which requires a lower computational cost than …
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Discontinuous Galerkin solutions of the Boltzmann equation: spectral collocation and moment methods
… Galerkin (DG) method to numerically solve the Boltzmann equation. Constructing numerical methods for this equation is a challenge, due in part to the kinetic theory description of moving particles, which relies on space, time, and velocity variables. Two novel approaches are presented and …
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Efficient numerical methods for solving the Boltzmann equation for small scale flows
The Navier-Stokes equations of continuum fluid mechanics fail to accurately describe dilute gas flows when the characteristic lengthscale of the system is on the order of (or smaller than) the molecular mean free path. At these lengthscales, gaseous hydrodynamics may be described by a kinetic …
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