Simulation of rare events by the stochastic weighted particle method for the Boltzmann equation

An extension of the stochastic weighted particle method for the numerical treatment of the Boltzmann equation is presented. A new procedure for modelling the inflow boundary conditions is introduced and its performance is tested in two-dimensional example with strong density gradients. A gain factor...

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Published inMathematical and computer modelling Vol. 33; no. 8; pp. 907 - 926
Main Authors Rjasanow, S., Wagner, W.
Format Journal Article
LanguageEnglish
Published Oxford Elsevier Ltd 01.04.2001
Elsevier Science
Subjects
Boltzmann equation
Exact sciences and technology
Fluid dynamics
Fundamental areas of phenomenology (including applications)
Integral equations
Mathematical analysis
Mathematics
Numerical experiments
Physics
Rare events
Rarefied gas dynamics
Sciences and techniques of general use
Stochastic particle method
Variance reduction
Stochastic particle method
Boltzmann equation
Rare events
Numerical experiments
Variance reduction
Gradient
Stochastic weighted particle method
Stochastic processes
Digital simulation
Boundary conditions
Two dimensional model
Numerical method
Computing
Stochastic method
Density
Rare event
Particles
Variance
Processing
Magnitudes
Kinetic equations
Collisions
Particle system
Inflow
Gain
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Abstract An extension of the stochastic weighted particle method for the numerical treatment of the Boltzmann equation is presented. A new procedure for modelling the inflow boundary conditions is introduced and its performance is tested in two-dimensional example with strong density gradients. A gain factor in computing time of several orders of magnitude is achieved in specific situations.
AbstractList An extension of the stochastic weighted particle method for the numerical treatment of the Boltzmann equation is presented. A new procedure for modelling the inflow boundary conditions is introduced and its performance is tested in two-dimensional example with strong density gradients. A gain factor in computing time of several orders of magnitude is achieved in specific situations.
Author Wagner, W.
Rjasanow, S.
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Cites_doi 10.1006/jcph.1996.0216
10.1006/jcph.1998.6011
10.1006/jcph.1998.6018
10.1006/jcph.1996.0057
10.1016/S0898-1221(97)00266-6
10.2514/3.832
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Issue 8
Keywords Stochastic particle method
Boltzmann equation
Rare events
Numerical experiments
Variance reduction
Gradient
Stochastic weighted particle method
Stochastic processes
Digital simulation
Boundary conditions
Two dimensional model
Numerical method
Computing
Stochastic method
Density
Rare event
Particles
Variance
Processing
Magnitudes
Kinetic equations
Collisions
Particle system
Inflow
Gain
Language English
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Elsevier Science
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References Boyd (BIB7) 1996; 10
Neunzert, Klar, Struckmeier (BIB6) 1996
Rjasanow, Wagner (BIB1) 1996; 124
Tiwari (BIB8) 1998; 144
Cercignani, Illner, Pulvirenti (BIB4) 1994
Rjasanow, Wagner (BIB2) 1998; 35
Bird (BIB5) 1994
Rjasanow, Wagner (BIB3) 1996; 128
Rjasanow, Schreiber, Wagner (BIB9) 1998; 145
Rjasanow (10.1016/S0895-7177(00)00289-2_BIB2) 1998; 35
Rjasanow (10.1016/S0895-7177(00)00289-2_BIB9) 1998; 145
Tiwari (10.1016/S0895-7177(00)00289-2_BIB8) 1998; 144
Rjasanow (10.1016/S0895-7177(00)00289-2_BIB1) 1996; 124
Neunzert (10.1016/S0895-7177(00)00289-2_BIB6) 1996
Boyd (10.1016/S0895-7177(00)00289-2_BIB7) 1996; 10
Rjasanow (10.1016/S0895-7177(00)00289-2_BIB3) 1996; 128
Cercignani (10.1016/S0895-7177(00)00289-2_BIB4) 1994
Bird (10.1016/S0895-7177(00)00289-2_BIB5) 1994
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Snippet An extension of the stochastic weighted particle method for the numerical treatment of the Boltzmann equation is presented. A new procedure for modelling the...
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SubjectTerms Boltzmann equation
Exact sciences and technology
Fluid dynamics
Fundamental areas of phenomenology (including applications)
Integral equations
Mathematical analysis
Mathematics
Numerical experiments
Physics
Rare events
Rarefied gas dynamics
Sciences and techniques of general use
Stochastic particle method
Variance reduction
Title Simulation of rare events by the stochastic weighted particle method for the Boltzmann equation
URI https://dx.doi.org/10.1016/S0895-7177(00)00289-2
Volume 33
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