A new Green's function Monte Carlo algorithm for the solution of the two-dimensional nonlinear Poisson–Boltzmann equation: Application to the modeling of the communication breakdown problem in space vehicles during re-entry

Journal Article · Sat Nov 01 00:00:00 EDT 2014 · Journal of Computational Physics

DOI:https://doi.org/10.1016/J.JCP.2014.07.042· OSTI ID:22382138

Chatterjee, Kausik ^[1]; Singh, Surendra ^[2]

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1. Strategic and Military Space Division, Space Dynamics Laboratory, North Logan, UT 84341 (United States)
2. Department of Electrical Engineering, The University of Tulsa, Tulsa, OK 74104 (United States)

The objective of this paper is the exposition of a recently-developed, novel Green's function Monte Carlo (GFMC) algorithm for the solution of nonlinear partial differential equations and its application to the modeling of the plasma sheath region around a cylindrical conducting object, carrying a potential and moving at low speeds through an otherwise neutral medium. The plasma sheath is modeled in equilibrium through the GFMC solution of the nonlinear Poisson–Boltzmann (NPB) equation. The traditional Monte Carlo based approaches for the solution of nonlinear equations are iterative in nature, involving branching stochastic processes which are used to calculate linear functionals of the solution of nonlinear integral equations. Over the last several years, one of the authors of this paper, K. Chatterjee has been developing a philosophically-different approach, where the linearization of the equation of interest is not required and hence there is no need for iteration and the simulation of branching processes. Instead, an approximate expression for the Green's function is obtained using perturbation theory, which is used to formulate the random walk equations within the problem sub-domains where the random walker makes its walks. However, as a trade-off, the dimensions of these sub-domains have to be restricted by the limitations imposed by perturbation theory. The greatest advantage of this approach is the ease and simplicity of parallelization stemming from the lack of the need for iteration, as a result of which the parallelization procedure is identical to the parallelization procedure for the GFMC solution of a linear problem. The application area of interest is in the modeling of the communication breakdown problem during a space vehicle's re-entry into the atmosphere. However, additional application areas are being explored in the modeling of electromagnetic propagation through the atmosphere/ionosphere in UHF/GPS applications.

• OSTI ID: 22382138
• Journal Information: Journal of Computational Physics, Vol. 276; Other Information: Copyright (c) 2014 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGORITHMS
APPROXIMATIONS
ATMOSPHERES
BOLTZMANN EQUATION
BRANCHING RATIO
COMMUNICATIONS
GLOBAL POSITIONING SYSTEM
GRAPH THEORY
GREEN FUNCTION
IONOSPHERE
ITERATIVE METHODS
MATHEMATICAL SOLUTIONS
MONTE CARLO METHOD
NONLINEAR PROBLEMS
PERTURBATION THEORY
PLASMA SHEATH
REENTRY
SPACE VEHICLES
STOCHASTIC PROCESSES
TWO-DIMENSIONAL CALCULATIONS