直接模拟蒙特卡罗方法(Direct Simulation Monte Carlo,DSMC)已经广泛用于稀薄空气动力学计算模拟,而直接数值求解Boltzmann方程目前还只局限于简单流动,比如一维线性问题.高度非线性、积分微分属性的Boltzmann方程的求解关键是碰撞积...直接模拟蒙特卡罗方法(Direct Simulation Monte Carlo,DSMC)已经广泛用于稀薄空气动力学计算模拟,而直接数值求解Boltzmann方程目前还只局限于简单流动,比如一维线性问题.高度非线性、积分微分属性的Boltzmann方程的求解关键是碰撞积分建模问题.最近,快速谱方法的提出和完善,使得对复杂的三维非线性问题直接求解Boltzmann方程带来了希望.相对于DSMC,快速谱方法具有数值上确定性的优势,在低速多尺度流动计算模拟上更为高效.本文介绍了快速谱方法在求解气体动理学方程的最新发展和成果,并探讨其应用前景.快速谱方法的推广应用使之真正成为DSMC的补充方法,现在面临的困难是需要发展新的气体动理学模型来描述多原子、多组分、稠密气体等.本文最后介绍了这方面的最新进展和直接求解Boltzmann模型方程气体动理论统一算法在模拟计算跨流域气体绕流及航天再入高超声速气动问题的应用.展开更多
A mathematical modelling of diagnostic biosensors system at three basic types of enzyme kinetics is discussed in the presence of diffusion. Enzyme kinetics is adopted to be first order, Michaelis-Menten and ping-pong ...A mathematical modelling of diagnostic biosensors system at three basic types of enzyme kinetics is discussed in the presence of diffusion. Enzyme kinetics is adopted to be first order, Michaelis-Menten and ping-pong mechanism. In this paper, approximate analytical solutions are obtained for the non-linear equations under steady-state conditions by using the new Homotopy perturbation method. Simple and closed forms of analytical expressions for concentrations of substrate, product and co-substrate and corresponding current response have been derived for all possible values of parameters. Furthermore, the numerical simulation of the problem is also reported here by using Matlab program. Good agreement between analytical and numerical results is noted.展开更多
Several kinds of explicit and implicit finite-difference schemes directly solving the discretized velocity distribution functions are designed with precision of different orders by analyzing the inner characteristics ...Several kinds of explicit and implicit finite-difference schemes directly solving the discretized velocity distribution functions are designed with precision of different orders by analyzing the inner characteristics of the gas-kinetic numerical algorithm for Boltzmann model equation. The peculiar flow phenomena and mechanism from various flow regimes are revealed in the numerical simulations of the unsteady Sod shock-tube problems and the two-dimensional channel flows with different Knudsen numbers. The numerical remainder-effects of the difference schemes are investigated aad analyzed based on the computed results. The ways of improving the computational efficiency of the gaskinetic numerical method and the computing principles of difference discretization are discussed.展开更多
The efficiency of recently developed gas-kinetic scheme for multimaterial flows is increased through the adoption of a new iteration method in the kinetic non-mixing Riemann solver and an interface sharpening reconstr...The efficiency of recently developed gas-kinetic scheme for multimaterial flows is increased through the adoption of a new iteration method in the kinetic non-mixing Riemann solver and an interface sharpening reconstruction method at a cell interface.The iteration method is used to determine the velocity of fluid interface,based on the force balance between both sides due to the incidence and bounce back of particles at the interface.An improved Aitken method is proposed with a simple hybrid of the modified Aitken method(Aitken-Chen)and the Steffensen method.Numerical tests validate its efficiency with significantly less calls to the function not only for the average number but also for the maximum.The new reconstruction is based on the tangent of hyperbola for interface capturing(THINC)but applied only to the volume fraction,which is very simple to be implemented under the stratified frame-work and capable of resolving fluid interface in mixture.Furthermore,the directional splitting is adopted rather than the previous quasi-one-dimensional method.Typical numerical tests,including several watergas shock tube flows,and the shock-water cylinder interaction flow show that the improved gas-kinetic scheme can capture fluid interfaces much sharper,while preserving the advantages of the original one.展开更多
A moment method with closures based on Gaussian quadrature formulas is proposed to solve the Boltzmann kinetic equation with a hard-sphere collision kernel for mono-dispersed particles.Different orders of accuracy in ...A moment method with closures based on Gaussian quadrature formulas is proposed to solve the Boltzmann kinetic equation with a hard-sphere collision kernel for mono-dispersed particles.Different orders of accuracy in terms of the moments of the velocity distribution function are considered,accounting for moments up to seventh order.Quadrature-based closures for four different models for inelastic collisionthe Bhatnagar-Gross-Krook,ES-BGK,the Maxwell model for hard-sphere collisions,and the full Boltzmann hard-sphere collision integral-are derived and compared.The approach is validated studying a dilute non-isothermal granular flow of inelastic particles between two stationary Maxwellian walls.Results obtained from the kinetic models are compared with the predictions of molecular dynamics(MD)simulations of a nearly equivalent system with finite-size particles.The influence of the number of quadrature nodes used to approximate the velocity distribution function on the accuracy of the predictions is assessed.Results for constitutive quantities such as the stress tensor and the heat flux are provided,and show the capability of the quadrature-based approach to predict them in agreement with the MD simulations under dilute conditions.展开更多
文摘直接模拟蒙特卡罗方法(Direct Simulation Monte Carlo,DSMC)已经广泛用于稀薄空气动力学计算模拟,而直接数值求解Boltzmann方程目前还只局限于简单流动,比如一维线性问题.高度非线性、积分微分属性的Boltzmann方程的求解关键是碰撞积分建模问题.最近,快速谱方法的提出和完善,使得对复杂的三维非线性问题直接求解Boltzmann方程带来了希望.相对于DSMC,快速谱方法具有数值上确定性的优势,在低速多尺度流动计算模拟上更为高效.本文介绍了快速谱方法在求解气体动理学方程的最新发展和成果,并探讨其应用前景.快速谱方法的推广应用使之真正成为DSMC的补充方法,现在面临的困难是需要发展新的气体动理学模型来描述多原子、多组分、稠密气体等.本文最后介绍了这方面的最新进展和直接求解Boltzmann模型方程气体动理论统一算法在模拟计算跨流域气体绕流及航天再入高超声速气动问题的应用.
文摘A mathematical modelling of diagnostic biosensors system at three basic types of enzyme kinetics is discussed in the presence of diffusion. Enzyme kinetics is adopted to be first order, Michaelis-Menten and ping-pong mechanism. In this paper, approximate analytical solutions are obtained for the non-linear equations under steady-state conditions by using the new Homotopy perturbation method. Simple and closed forms of analytical expressions for concentrations of substrate, product and co-substrate and corresponding current response have been derived for all possible values of parameters. Furthermore, the numerical simulation of the problem is also reported here by using Matlab program. Good agreement between analytical and numerical results is noted.
基金supported by the National Natural Science Foundation of China (No.10621062)the Research Fund for Next Generation of General Armament Department (No.9140A13050207KG29)
文摘Several kinds of explicit and implicit finite-difference schemes directly solving the discretized velocity distribution functions are designed with precision of different orders by analyzing the inner characteristics of the gas-kinetic numerical algorithm for Boltzmann model equation. The peculiar flow phenomena and mechanism from various flow regimes are revealed in the numerical simulations of the unsteady Sod shock-tube problems and the two-dimensional channel flows with different Knudsen numbers. The numerical remainder-effects of the difference schemes are investigated aad analyzed based on the computed results. The ways of improving the computational efficiency of the gaskinetic numerical method and the computing principles of difference discretization are discussed.
基金supported by Science Challenge Project(TZ2016001)National Natural Science Foundation of China(U1430235)Special Program for Applied Research on Super Computation of the NSFC-Guangdong Joint Fund(the second phase).
文摘The efficiency of recently developed gas-kinetic scheme for multimaterial flows is increased through the adoption of a new iteration method in the kinetic non-mixing Riemann solver and an interface sharpening reconstruction method at a cell interface.The iteration method is used to determine the velocity of fluid interface,based on the force balance between both sides due to the incidence and bounce back of particles at the interface.An improved Aitken method is proposed with a simple hybrid of the modified Aitken method(Aitken-Chen)and the Steffensen method.Numerical tests validate its efficiency with significantly less calls to the function not only for the average number but also for the maximum.The new reconstruction is based on the tangent of hyperbola for interface capturing(THINC)but applied only to the volume fraction,which is very simple to be implemented under the stratified frame-work and capable of resolving fluid interface in mixture.Furthermore,the directional splitting is adopted rather than the previous quasi-one-dimensional method.Typical numerical tests,including several watergas shock tube flows,and the shock-water cylinder interaction flow show that the improved gas-kinetic scheme can capture fluid interfaces much sharper,while preserving the advantages of the original one.
文摘A moment method with closures based on Gaussian quadrature formulas is proposed to solve the Boltzmann kinetic equation with a hard-sphere collision kernel for mono-dispersed particles.Different orders of accuracy in terms of the moments of the velocity distribution function are considered,accounting for moments up to seventh order.Quadrature-based closures for four different models for inelastic collisionthe Bhatnagar-Gross-Krook,ES-BGK,the Maxwell model for hard-sphere collisions,and the full Boltzmann hard-sphere collision integral-are derived and compared.The approach is validated studying a dilute non-isothermal granular flow of inelastic particles between two stationary Maxwellian walls.Results obtained from the kinetic models are compared with the predictions of molecular dynamics(MD)simulations of a nearly equivalent system with finite-size particles.The influence of the number of quadrature nodes used to approximate the velocity distribution function on the accuracy of the predictions is assessed.Results for constitutive quantities such as the stress tensor and the heat flux are provided,and show the capability of the quadrature-based approach to predict them in agreement with the MD simulations under dilute conditions.
