The [Delta]-[epsilon] method for the Boltzmann equation

Journal Article · Tue Feb 01 04:00:00 EST 1994 · Journal of Computational Physics; (United States)

DOI:https://doi.org/10.1006/jcph.1994.1030· OSTI ID:7032756

Tan, Zhiqiang; Varghese, P L ^[1]

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1. Univ of Texas, Austin (United States)

A new numerical method is proposed to solve the Boltzmann equation. A frame is set up by using a discrete velocity approximation in the infinite velocity space, but by considering only those distribution function points which are not too small. The distribution function points may occur anywhere in the infinite discrete velocity space and are not constrained to a pre-specified region. A fourth-order finite difference is used for the convection terms. A Monte Carlo-like method is applied to the discrete velocity model of the collision integral. The effort of the method is proportional to the number of discrete points. Numerical examples are given for the full Boltzmann equation and results for some benchmark problems are compared with analytical or prior solutions. 25 refs., 21 figs.

• OSTI ID: 7032756
• Journal Information: Journal of Computational Physics; (United States), Journal Name: Journal of Computational Physics; (United States) Vol. 110:2; ISSN 0021-9991; ISSN JCTPAH
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
420400 -- Engineering-- Heat Transfer & Fluid Flow
663610* -- Neutron Physics-- (1992-)
73 NUCLEAR PHYSICS AND RADIATION PHYSICS
99 GENERAL AND MISCELLANEOUS
990200 -- Mathematics & Computers
BOLTZMANN EQUATION
CALCULATION METHODS
COMPUTERIZED SIMULATION
DIFFERENTIAL EQUATIONS
EQUATIONS
FINITE DIFFERENCE METHOD
ITERATIVE METHODS
MONTE CARLO METHOD
NEUTRAL-PARTICLE TRANSPORT
NEUTRON TRANSPORT
NUMERICAL SOLUTION
PARTIAL DIFFERENTIAL EQUATIONS
RADIATION TRANSPORT
SIMULATION