Based on the stability analysis with no linearization and expansion, it is argued that instability in the lattice BGK model is originated from the linear relaxation hypothesis of collision in the model. The hypothesis...Based on the stability analysis with no linearization and expansion, it is argued that instability in the lattice BGK model is originated from the linear relaxation hypothesis of collision in the model. The hypothesis stands up only when the deviation from the local equilibrium is weak. In this case the computation is absolutely stable for real fluids. But for flows of high Reynolds number, this hypothesis is violated and then instability takes place physically. By performing a transformation a quantified stability criteria is put forward without those approximation. From the criteria a sufficient condition for stability can be obtained and serve as an estimation of the limited Reynolds number as high as possible.展开更多
The Boltzmann-Bhatnagar-Gross-Krook（BGK）model is investigated for its validity regarding the collision term approximation through relaxation evaluation. The evaluation is based on theoretical analysis and numerical ...The Boltzmann-Bhatnagar-Gross-Krook（BGK）model is investigated for its validity regarding the collision term approximation through relaxation evaluation. The evaluation is based on theoretical analysis and numerical comparison between the BGK and direct simulation Monte Carlo（DSMC） results for three specifically designed relaxation problems. In these problems, one or half component of the velocity distribution is characterized by another Maxwellian distribution with a different temperature. It is analyzed that the relaxation time in the BGK model is unequal to the molecular mean collision time. Relaxation of component distribution fails to involve enough contribution from other component distributions, which makes the BGK model unable to capture details of velocity distribution, especially when discontinuity exists in distribution. The BGK model,however, predicts satisfactory results including fluxes during relaxation when the temperature difference is small. Particularly, the model-induced error in the BGK model increases with the temperature difference, thus the model is more reliable for low-speed rarefied flows than for hypersonic flows.展开更多
In the present paper the rarefied gas how caused by the sudden change of the wall temperature and the Rayleigh problem are simulated by the DSMC method which has been validated by experiments both in global flour fiel...In the present paper the rarefied gas how caused by the sudden change of the wall temperature and the Rayleigh problem are simulated by the DSMC method which has been validated by experiments both in global flour field and velocity distribution function level. The comparison of the simulated results with the accurate numerical solutions of the B-G-K model equation shows that near equilibrium the BG-K equation with corrected collision frequency can give accurate result but as farther away from equilibrium the B-G-K equation is not accurate. This is for the first time that the error caused by the B-G-K model equation has been revealed.展开更多
A lattice Boltzmann numerical modeling method was developed to predict skin concentration after topical application of a drug on the skin. The method is based on D2Q9 lattice spaces associated with the Bhatnagar-Gross...A lattice Boltzmann numerical modeling method was developed to predict skin concentration after topical application of a drug on the skin. The method is based on D2Q9 lattice spaces associated with the Bhatnagar-Gross-Krook(BGK) collision term to solve the convection-diffusion equation(CDE). A simulation was carried out in different ranges of the value of bound γ, which is related to skin capillary clearance and the volume of diffusion during a percutaneous absorption process. When a typical drug is used on the skin, the value of γ corresponds to the amount of drug absorbed by the blood and the absorption of the drug added to the skin. The effect of γ was studied for when the region of skin contact is a line segment on the skin surface.展开更多
In this paper a Lattice Bhatager-Gross-Krook (LBGK) model to simulateincompressible flow is developed. The basic idea is to explicitly eliminate the compressible effect,due to the density fluctuation in the existing L...In this paper a Lattice Bhatager-Gross-Krook (LBGK) model to simulateincompressible flow is developed. The basic idea is to explicitly eliminate the compressible effect,due to the density fluctuation in the existing LBGK models. In the proposed incompressible LBGKmodel, the pressure p instead of the constant mass density ρ_0 is the independent dynamic variable.The incompressible Navier-Stokes equations are exactly derived from this incompressible LBGK model.In order to test the LBGK model, the plane Poiseuille flow driven either by pressure gradient or afixed velocity profile at entrance as well as the 2-D Womersley flow are simulated. The numericalresults are found to be in excellent agreement with theory and the results of previous studies.展开更多
The incompressible lattice Bhatnager-Gross-Krook （BGK） model of computational fluid dynamics, from which the unsteady incompressible Navier-Stokes equations can be exactly derived with the limit of small Mach number...The incompressible lattice Bhatnager-Gross-Krook （BGK） model of computational fluid dynamics, from which the unsteady incompressible Navier-Stokes equations can be exactly derived with the limit of small Mach number, was established in continuous casting mold. An asymmetric flow pattern in the two-dimensional central plane of continuous slab casting mold was simulated, and the flow pattern is not stationary but changes over frequently if the Reynolds number is larger than 3000 or so. The results are found to be in excellent agreement with previous experimental results.展开更多
As is known,the numerical stiffness arising from the small mean free path is one of the main difficulties in the kinetic equations.In this paper,we derive both the split and the unsplit schemes for the linear semicond...As is known,the numerical stiffness arising from the small mean free path is one of the main difficulties in the kinetic equations.In this paper,we derive both the split and the unsplit schemes for the linear semiconductor Boltzmann equation with a diffusive scaling.In the two schemes,the anisotropic collision operator is realized by the“BGK”-penalty method,which is proposed by Filbet and Jin[F.Filbet and S.Jin,J.Comp.Phys.229(20),7625-7648,2010]for the kinetic equations and the related problems having stiff sources.According to the numerical results,both of the schemes are shown to be uniformly convergent and asymptotic-preserving.Besides,numerical evidences suggest that the unsplit scheme has a better numerical stability than the split scheme.展开更多
文摘Based on the stability analysis with no linearization and expansion, it is argued that instability in the lattice BGK model is originated from the linear relaxation hypothesis of collision in the model. The hypothesis stands up only when the deviation from the local equilibrium is weak. In this case the computation is absolutely stable for real fluids. But for flows of high Reynolds number, this hypothesis is violated and then instability takes place physically. By performing a transformation a quantified stability criteria is put forward without those approximation. From the criteria a sufficient condition for stability can be obtained and serve as an estimation of the limited Reynolds number as high as possible.
基金supported by the National Natural Science Foundation of China(91116013,11372325,and 11111120080)
文摘The Boltzmann-Bhatnagar-Gross-Krook（BGK）model is investigated for its validity regarding the collision term approximation through relaxation evaluation. The evaluation is based on theoretical analysis and numerical comparison between the BGK and direct simulation Monte Carlo（DSMC） results for three specifically designed relaxation problems. In these problems, one or half component of the velocity distribution is characterized by another Maxwellian distribution with a different temperature. It is analyzed that the relaxation time in the BGK model is unequal to the molecular mean collision time. Relaxation of component distribution fails to involve enough contribution from other component distributions, which makes the BGK model unable to capture details of velocity distribution, especially when discontinuity exists in distribution. The BGK model,however, predicts satisfactory results including fluxes during relaxation when the temperature difference is small. Particularly, the model-induced error in the BGK model increases with the temperature difference, thus the model is more reliable for low-speed rarefied flows than for hypersonic flows.
基金The project supported by the National Natural Science Foundation of China (19772059, 19889209)
文摘In the present paper the rarefied gas how caused by the sudden change of the wall temperature and the Rayleigh problem are simulated by the DSMC method which has been validated by experiments both in global flour field and velocity distribution function level. The comparison of the simulated results with the accurate numerical solutions of the B-G-K model equation shows that near equilibrium the BG-K equation with corrected collision frequency can give accurate result but as farther away from equilibrium the B-G-K equation is not accurate. This is for the first time that the error caused by the B-G-K model equation has been revealed.
基金supported by the National Research Foundation of Korea(NRF)grant funded by the Korean government(MSIT)(2011-0030013 and 2018R1A2B2007117)
文摘A lattice Boltzmann numerical modeling method was developed to predict skin concentration after topical application of a drug on the skin. The method is based on D2Q9 lattice spaces associated with the Bhatnagar-Gross-Krook(BGK) collision term to solve the convection-diffusion equation(CDE). A simulation was carried out in different ranges of the value of bound γ, which is related to skin capillary clearance and the volume of diffusion during a percutaneous absorption process. When a typical drug is used on the skin, the value of γ corresponds to the amount of drug absorbed by the blood and the absorption of the drug added to the skin. The effect of γ was studied for when the region of skin contact is a line segment on the skin surface.
文摘In this paper a Lattice Bhatager-Gross-Krook (LBGK) model to simulateincompressible flow is developed. The basic idea is to explicitly eliminate the compressible effect,due to the density fluctuation in the existing LBGK models. In the proposed incompressible LBGKmodel, the pressure p instead of the constant mass density ρ_0 is the independent dynamic variable.The incompressible Navier-Stokes equations are exactly derived from this incompressible LBGK model.In order to test the LBGK model, the plane Poiseuille flow driven either by pressure gradient or afixed velocity profile at entrance as well as the 2-D Womersley flow are simulated. The numericalresults are found to be in excellent agreement with theory and the results of previous studies.
基金Project supported by the National Natural Science Foundation of China (Grant No: 50474088).
文摘The incompressible lattice Bhatnager-Gross-Krook （BGK） model of computational fluid dynamics, from which the unsteady incompressible Navier-Stokes equations can be exactly derived with the limit of small Mach number, was established in continuous casting mold. An asymmetric flow pattern in the two-dimensional central plane of continuous slab casting mold was simulated, and the flow pattern is not stationary but changes over frequently if the Reynolds number is larger than 3000 or so. The results are found to be in excellent agreement with previous experimental results.
文摘As is known,the numerical stiffness arising from the small mean free path is one of the main difficulties in the kinetic equations.In this paper,we derive both the split and the unsplit schemes for the linear semiconductor Boltzmann equation with a diffusive scaling.In the two schemes,the anisotropic collision operator is realized by the“BGK”-penalty method,which is proposed by Filbet and Jin[F.Filbet and S.Jin,J.Comp.Phys.229(20),7625-7648,2010]for the kinetic equations and the related problems having stiff sources.According to the numerical results,both of the schemes are shown to be uniformly convergent and asymptotic-preserving.Besides,numerical evidences suggest that the unsplit scheme has a better numerical stability than the split scheme.
