Journal ArticleDOI
A Gaussian quadrature procedure for use in the solution of the Boltzmann equation and related problems
TLDR
In this article, a new Gaussian quadrature procedure was developed for integrals of the form ∫ 0 ∞ e − y 2 y p ( y ) dy for p = 0, 1 and 2.About:
This article is published in Journal of Computational Physics.The article was published on 1981-06-01. It has received 183 citations till now. The article focuses on the topics: Gauss–Kronrod quadrature formula & Gauss–Jacobi quadrature.read more
Citations
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Journal ArticleDOI
Discrete singular convolution for the solution of the Fokker–Planck equation
TL;DR: In this paper, a discrete singular convolution algorithm for solving the Fokker-Planck equation is presented, where singular kernels of the Hilbert-type and the delta type are presented for numerical computations.
Journal ArticleDOI
The Lagrange-mesh method
TL;DR: The Lagrange-mesh method as mentioned in this paper is an approximate variational method taking the form of equations on a grid thanks to the use of a Gauss-quadrature approximation.
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Study on gas kinetic unified algorithm for flows from rarefied transition to continuum
Zhi-Hui Li,Han-Xin Zhang +1 more
TL;DR: In this article, the authors presented a modified BGK equation adapted to various flow regimes by the aid of the basic characteristics on molecular movement and collision approaching to equilibrium, and the discrete velocity ordinate method was developed and applied to the velocity distribution function to remove its continuous dependency on the velocity space.
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Gas-kinetic numerical studies of three-dimensional complex flows on spacecraft re-entry
Zhi-Hui Li,Han-Xin Zhang +1 more
TL;DR: The gas-kinetic numerical algorithm solving the Boltzmann model equation is extended and developed to study the three-dimensional hypersonic flows of spacecraft re-entry into the atmosphere in perfect gas and the simplified velocity distribution function equation for various flow regimes is presented.
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A unified approach for the solution of the Fokker-Planck equation
TL;DR: In this article, the authors explored the use of a discrete singular convolution algorithm as a unified approach for numerical integration of the Fokker-Planck equation and demonstrated that different implementations of the present algorithm, such as global, local, Galerkin, collocation and finite difference, can be deduced from a single starting point.
References
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Journal ArticleDOI
Methods of Numerical Integration.
Book
Rarefied Gas Dynamics
TL;DR: In this paper, the authors present a simulation of a free jet expansion of a high-energy scattering of molecular beams in the presence of high-temperature Viscosity cross sections.
Journal ArticleDOI
Construction of Gauss-Christoffel quadrature formulas
TL;DR: The Gauss-Christoffel quadrature formula (GCE) as discussed by the authors is defined as a Gauss Christoffel formula with maximum degree of exactness, i.e. if (1.1) is an exact equality whenever f is a polynomial of degree 2n 1.