A STOCHASTIC MATHEMATICAL MODEL ON THE KINETIC THEORY OF TEST PARTICLES IN THE FLOW FIELD OF THE DISCRETE BOLTZMANN EQUATION

1984 ◽  
pp. 311-315
Author(s):  
F. Piazzese
Keyword(s):  
Mathematical Model ◽  
Boltzmann Equation ◽  
Flow Field ◽  
Kinetic Theory ◽  
Test Particles ◽  
Discrete Boltzmann Equation

A NEW DISCRETIZED MODEL IN NONLINEAR KINETIC THEORY—THE SEMICONTINUOUS BOLTZMANN EQUATION

1991 ◽  
Vol 01 (01) ◽  
pp. 113-123 ◽  
Author(s):  
N. BELLOMO ◽  
E. LONGO
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Boltzmann Equation ◽  
Kinetic Theory ◽  
Continuous Dependence ◽  
Modeling And Analysis ◽  
Collision Invariants ◽  
The Mathematical Model ◽  
Nonlinear Kinetic ◽  
Discretized Model

This paper deals with the mathematical modeling and analysis of a new model of the Boltzmann equation with a finite number of velocity moduli, but with a continuous dependence on the velocity directions. The mathematical model is derived in the first part of the paper. Then the analysis of the equilibrium Maxwellian state is dealt with in the second part of the paper with the purpose of showing that the space of collision invariants is the correct one.

A DISCRETE BOLTZMANN EQUATION BASED ON HEXAGONS

2003 ◽  
Vol 13 (11) ◽  
pp. 1537-1563 ◽  
Author(s):  
LAEK S. ANDALLAH ◽  
HANS BABOVSKY
Keyword(s):  
Boltzmann Equation ◽  
Kinetic Theory ◽  
Velocity Space ◽  
Equilibrium Solutions ◽  
Collision Invariants ◽  
Linearized Problem ◽  
Hexagonal Grids ◽  
H Theorem ◽  
Basic Features ◽  
Discrete Boltzmann Equation

We develop the theory of a Boltzmann equation which is based on a hexagonal discretization of the velocity space. We prove that such a model contains all the basic features of classical kinetic theory, like collision invariants, H-theorem, equilibrium solutions, features of the linearized problem etc. This theory includes the infinite as well as finite hexagonal grids which may be used for numerical purposes.

Boltzmann’s Kinetic Theory

2018 ◽  
Author(s):  
Sauro Succi
Keyword(s):  
Boltzmann Equation ◽  
Kinetic Theory ◽  
Statistical Physics ◽  
Neutron Transport ◽  
Condensed Matter ◽  
Relativistic Fluids ◽  
Classical Statistical Mechanics ◽  
Dilute Gas ◽  
Equilibrium Processes ◽  
The Boltzmann Equation

Kinetic theory is the branch of statistical physics dealing with the dynamics of non-equilibrium processes and their relaxation to thermodynamic equilibrium. Established by Ludwig Boltzmann (1844–1906) in 1872, his eponymous equation stands as its mathematical cornerstone. Originally developed in the framework of dilute gas systems, the Boltzmann equation has spread its wings across many areas of modern statistical physics, including electron transport in semiconductors, neutron transport, quantum-relativistic fluids in condensed matter and even subnuclear plasmas. In this Chapter, a basic introduction to the Boltzmann equation in the context of classical statistical mechanics shall be provided.

Discrete Boltzmann Equation model of polydisperse shallow granular flows

2019 ◽  
Vol 113 ◽  
pp. 107-116 ◽  
Author(s):  
Michele La Rocca ◽  
Andrea Montessori ◽  
Pietro Prestininzi ◽  
Lakshmanan Elango
Keyword(s):  
Boltzmann Equation ◽  
Granular Flows ◽  
Equation Model ◽  
Discrete Boltzmann Equation

scholarly journals Influence of M-EMS on Fluid Flow and Initial Solidification in Slab Continuous Casting

Materials ◽  
2021 ◽  
Vol 14 (13) ◽  
pp. 3681
Author(s):  
Guoliang Liu ◽  
Haibiao Lu ◽  
Bin Li ◽  
Chenxi Ji ◽  
Jiangshan Zhang ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Flow Field ◽  
Continuous Casting ◽  
Casting Speed ◽  
Liquid Pool ◽  
Industrial Test ◽  
Magnetic Flux Density ◽  
Continuous Casting Mold ◽  
Slab Continuous Casting ◽  
Initial Solidification

A mathematical model coupled with electromagnetic field has been developed to simulate the transient turbulence flow and initial solidification in a slab continuous casting mold under different electromagnetic stirring (EMS) currents and casting speeds. Through comparing the magnetic flux density, flow field with measured results, the reliability of the mathematical model is proved. The uniform index of solidified shell thickness has been introduced to judge the uniformity of the solidified shell. The results show that a horizonal recirculation flow has been generated when EMS is applied, and either accelerated or decelerated regions of flow field are formed in the liquid pool. Large EMS current and low casting speed may cause the plug flow near the mold narrow face and a suitable EMS current can benefit to the uniform growth of solidified shell. Meanwhile, an industrial test exhibits that EMS can weaken the level fluctuation and number density of inclusion. Overall, a rational EMS current range is gained, when the casting speed is 1.2 m/min, the rational EMS current is 500–600 A.

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