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
Aim.The well known JST(Jameson-Schmidt-Turkel) scheme requires the use of a dissipation term.We propose using gas-kinetic BGK(Bhatnagar-Gross-Krook) method,which is based on the more fundamental Boltzmann equation,in ...Aim.The well known JST(Jameson-Schmidt-Turkel) scheme requires the use of a dissipation term.We propose using gas-kinetic BGK(Bhatnagar-Gross-Krook) method,which is based on the more fundamental Boltzmann equation,in order to obviate the use of dissipation term and obtain,we believe,an improved solution.Section 1 deals essentially with three things:(1) as analytical solution of molecular probability density function at the cell interface has been obtained by the Boltzmann equation with BGK model,we can compute the flux term by integrating the density function in the phase space;eqs.(8) and(11) require careful attention;(2) the integrations can be expressed as the moments of Maxwellian distribution with different limits according to the analytical solution;eqs.(9) and(10) require careful attention;(3) the discrete equation by finite volume method can be solved using the time marching method.Computations are performed by the BGK method for the Sod′s shock tube problem and a two-dimensional shock reflection problem.The results are compared with those of the conventional JST scheme in Figs.1 and 2.The BGK method provides better resolution of shock waves and other features of the flow fields.展开更多
Based on the Bhatnagar-Gross-Krook distillation for two components in the presence equation, a new scheme of wiped-film molecular of inert gas is developed. The equations in the scheme are solved numerically by the me...Based on the Bhatnagar-Gross-Krook distillation for two components in the presence equation, a new scheme of wiped-film molecular of inert gas is developed. The equations in the scheme are solved numerically by the method of finite difference and iteration. The new scheme is used to simulate the molecular distillation of dibutyl phthalate and dibutyl sebacate （ DBP-DBS ） mixture. The effects of the inert gas pressure, the distance between the evaporation surface and condensation surface, the rotation rate of blade, and the number of blades on the distillation rate and separation factor are discussed.展开更多
In recent years, the Lattice Boltzmann Method (LBM) has developed into an alternative and promising numerical scheme for simulating fluid flows and modeling physics in fluids. In order to propose LBM for high Reynolds...In recent years, the Lattice Boltzmann Method (LBM) has developed into an alternative and promising numerical scheme for simulating fluid flows and modeling physics in fluids. In order to propose LBM for high Reynolds number fluid flow applications, a subgrid turbulence model for LBM was introduced based on standard Smagorinsky subgrid model and Lattice Bhatnagar-Gross-Krook (LBGK) model. The subgrid LBGK model was subsequently used to simulate the two-dimensional driven cavity flow at high Reynolds numbers. The simulation results including distribution of stream lines, dimensionless velocities distribution, values of stream function, as well as location of vertex center, were compared with benchmark solutions, with satisfactory agreements.展开更多
In this paper, a lattice Boltzmann equation （LBE） model with multiple-relaxation-time （MRT） colli- sion operator is developed based on the Enskog theory for isothermal nonideal mixtures, which is an extension of t...In this paper, a lattice Boltzmann equation （LBE） model with multiple-relaxation-time （MRT） colli- sion operator is developed based on the Enskog theory for isothermal nonideal mixtures, which is an extension of the previous single relaxation time （SRT） LBE model （Guo and Zhao in Phys Rev E 68：035302, 2003）. The present MRT-LBE model overcomes some inherent defects of the original SRT-LBE model such as the fixed Schmidt num- ber and limited viscosity ratio. It is also interestingly shown that the widely used Shan-Chen （SC） model, which is constructed heuristically based on the pseudo-potential concept, can also be regarded as a special case of the present model, and thus putting a solid foundation for this well-accepted multiphase LBE model. A series of nu- merical simulations, including the static droplet and lay- ered co-current flow, are conducted to test the applicability of the present model for immiscible fluids with different Schmidt numbers and large viscosity ratio, which may be difficult for the original SRT-LBE model and the SC model.展开更多
A Coupled Lattice Bhatnagar Gross Krook （CLBGK） model was proposed with a robust boundary scheme to model the Bossinesq incompressible flows. The LBGK method is a powerful approach, but is also computationally deman...A Coupled Lattice Bhatnagar Gross Krook （CLBGK） model was proposed with a robust boundary scheme to model the Bossinesq incompressible flows. The LBGK method is a powerful approach, but is also computationally demanding. Therefore, parallel computing was implemented, and the codes were run on the parallel computer “Lenovo DeepComp 1800” with 24 nodes written in C＋＋ using the Message Passing Interface （MPI） library. Numerical results for natural convection in a cavity with the Rayleigh number （ Ra ） ranging from 10^6 to 4× 10^10 were presented, and found to agree well with the previous work. And with the increase of the resolution rate, the accuracy has been greatly improved. In addition, new models were set up by applying different equilibriums to the CLBGK model to simulate the same problem, which all yield sound results.展开更多
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Aim.The well known JST(Jameson-Schmidt-Turkel) scheme requires the use of a dissipation term.We propose using gas-kinetic BGK(Bhatnagar-Gross-Krook) method,which is based on the more fundamental Boltzmann equation,in order to obviate the use of dissipation term and obtain,we believe,an improved solution.Section 1 deals essentially with three things:(1) as analytical solution of molecular probability density function at the cell interface has been obtained by the Boltzmann equation with BGK model,we can compute the flux term by integrating the density function in the phase space;eqs.(8) and(11) require careful attention;(2) the integrations can be expressed as the moments of Maxwellian distribution with different limits according to the analytical solution;eqs.(9) and(10) require careful attention;(3) the discrete equation by finite volume method can be solved using the time marching method.Computations are performed by the BGK method for the Sod′s shock tube problem and a two-dimensional shock reflection problem.The results are compared with those of the conventional JST scheme in Figs.1 and 2.The BGK method provides better resolution of shock waves and other features of the flow fields.
基金Supported by National Natural Science Foundation of China(No. 20136010).
文摘Based on the Bhatnagar-Gross-Krook distillation for two components in the presence equation, a new scheme of wiped-film molecular of inert gas is developed. The equations in the scheme are solved numerically by the method of finite difference and iteration. The new scheme is used to simulate the molecular distillation of dibutyl phthalate and dibutyl sebacate （ DBP-DBS ） mixture. The effects of the inert gas pressure, the distance between the evaporation surface and condensation surface, the rotation rate of blade, and the number of blades on the distillation rate and separation factor are discussed.
文摘In recent years, the Lattice Boltzmann Method (LBM) has developed into an alternative and promising numerical scheme for simulating fluid flows and modeling physics in fluids. In order to propose LBM for high Reynolds number fluid flow applications, a subgrid turbulence model for LBM was introduced based on standard Smagorinsky subgrid model and Lattice Bhatnagar-Gross-Krook (LBGK) model. The subgrid LBGK model was subsequently used to simulate the two-dimensional driven cavity flow at high Reynolds numbers. The simulation results including distribution of stream lines, dimensionless velocities distribution, values of stream function, as well as location of vertex center, were compared with benchmark solutions, with satisfactory agreements.
基金This work was financially supported by the National Natural Science Foundation of China （51125024） and the National Basic Research Programme of China （2011CB707305）.
文摘In this paper, a lattice Boltzmann equation （LBE） model with multiple-relaxation-time （MRT） colli- sion operator is developed based on the Enskog theory for isothermal nonideal mixtures, which is an extension of the previous single relaxation time （SRT） LBE model （Guo and Zhao in Phys Rev E 68：035302, 2003）. The present MRT-LBE model overcomes some inherent defects of the original SRT-LBE model such as the fixed Schmidt num- ber and limited viscosity ratio. It is also interestingly shown that the widely used Shan-Chen （SC） model, which is constructed heuristically based on the pseudo-potential concept, can also be regarded as a special case of the present model, and thus putting a solid foundation for this well-accepted multiphase LBE model. A series of nu- merical simulations, including the static droplet and lay- ered co-current flow, are conducted to test the applicability of the present model for immiscible fluids with different Schmidt numbers and large viscosity ratio, which may be difficult for the original SRT-LBE model and the SC model.
文摘A Coupled Lattice Bhatnagar Gross Krook （CLBGK） model was proposed with a robust boundary scheme to model the Bossinesq incompressible flows. The LBGK method is a powerful approach, but is also computationally demanding. Therefore, parallel computing was implemented, and the codes were run on the parallel computer “Lenovo DeepComp 1800” with 24 nodes written in C＋＋ using the Message Passing Interface （MPI） library. Numerical results for natural convection in a cavity with the Rayleigh number （ Ra ） ranging from 10^6 to 4× 10^10 were presented, and found to agree well with the previous work. And with the increase of the resolution rate, the accuracy has been greatly improved. In addition, new models were set up by applying different equilibriums to the CLBGK model to simulate the same problem, which all yield sound results.
