This paper presents the numerical simulations of two Richtmyer-Meshkov （RM） instability experiments using the conservative front-tracking method developed in （Mao, D. Towards front-tracking based on conservation in...This paper presents the numerical simulations of two Richtmyer-Meshkov （RM） instability experiments using the conservative front-tracking method developed in （Mao, D. Towards front-tracking based on conservation in two space dimensions II, tracking discontinuities in capturing fashion. J. Comput. Phys., 226, 1550-1588 （2007））. The numerical results are compared with those obtained in （Holmes, R. L., Grove, J. W., and Sharp, D. H. Numerical investigation of Richtmyer-Meshkov instability using front-tracking. J. Fluid Mech., 301, 51-64 （1995））. The present simulations are generally in good agreement with those obtained by Holmes et al., and also capture the nonlinear and compessive phenomenon, i.e., the self-interactions of the transmitted and reflected wave edges, which was pointed out by Holmes et al. as the cause of the deceleration of the interfaces. However, the perturbation amplitudes and the amplitude growth rates of the interfaces obtained with the present conservative front-tracking method are a bit larger than those obtained by Holmes et al.展开更多
We developed a three-dimensional multi-relaxation-time lattice Boltzmann method for incompressible and immiscible two-phase flow by coupling with a front-tracking technique. The flow field was simulated by using an Eu...We developed a three-dimensional multi-relaxation-time lattice Boltzmann method for incompressible and immiscible two-phase flow by coupling with a front-tracking technique. The flow field was simulated by using an Eulerian grid, an adaptive unstructured triangular Lagrangian grid was applied to track explicitly the motion of the two-fluid interface, and an indicator function was introduced to update accurately the fluid properties. The surface tension was computed directly on a triangular Lagrangian grid, and then the surface tension was distributed to the background Eulerian grid. Three benchmarks of two-phase flow, including the Laplace law for a stationary drop, the oscillation of a three-dimensional ellipsoidal drop, and the drop deformation in a shear flow, were simulated to validate the present model.展开更多
An approach to deal with movings and collisions of arbitrary many discontinuities in the conservative front tracking method is developed. Using this approach one may develop an ＂all-purposed and robust＂ front-tracki...An approach to deal with movings and collisions of arbitrary many discontinuities in the conservative front tracking method is developed. Using this approach one may develop an ＂all-purposed and robust＂ front-tracking algorithm. The algorithm with this approach may have some inconsistency and thus will have 0（1） magnitude errors in some grid cells at sometimes. Nevertheless, these errors will be eliminated by the conservation-preserving property of the front-tracking method in the following computation. Numerical examples are presented to illustrate the efficiency of the approach.展开更多
In this paper,we present a finite difference method to track a network of curves whose motion is determined by mean curvature.To study the effect of inhomogeneous surface tension on the evolution of the network of cu...In this paper,we present a finite difference method to track a network of curves whose motion is determined by mean curvature.To study the effect of inhomogeneous surface tension on the evolution of the network of curves,we include surfactant which can diffuse along the curves.The governing equations consist of one parabolic equation for the curve motion coupled with a convection-diffusion equation for the surfactant concentration along each curve.Our numerical method is based on a direct discretization of the governing equations which conserves the total surfactant mass in the curve network.Numerical experiments are carried out to examine the effects of inhomogeneous surface tension on the motion of the network,including the von Neumann law for cell growth in two space dimensions.展开更多
We present a variable time step,fully adaptive in space,hybrid method for the accurate simulation of incompressible two-phase flows in the presence of surface tension in two dimensions.The method is based on the hybri...We present a variable time step,fully adaptive in space,hybrid method for the accurate simulation of incompressible two-phase flows in the presence of surface tension in two dimensions.The method is based on the hybrid level set/front-tracking approach proposed in[H.D.Ceniceros and A.M.Roma,J.Comput.Phys.,205,391-400,2005].Geometric,interfacial quantities are computed from front-tracking via the immersed-boundary setting while the signed distance(level set)function,which is evaluated fast and to machine precision,is used as a fluid indicator.The surface tension force is obtained by employing the mixed Eulerian/Lagrangian representation introduced in[S.Shin,S.I.Abdel-Khalik,V.Daru and D.Juric,J.Comput.Phys.,203,493-516,2005]whose success for greatly reducing parasitic currents has been demonstrated.The use of our accurate fluid indicator together with effective Lagrangian marker control enhance this parasitic current reduction by several orders of magnitude.To resolve accurately and efficiently sharp gradients and salient flow features we employ dynamic,adaptive mesh refinements.This spatial adaption is used in concert with a dynamic control of the distribution of the Lagrangian nodes along the fluid interface and a variable time step,linearly implicit time integration scheme.We present numerical examples designed to test the capabilities and performance of the proposed approach as well as three applications:the long-time evolution of a fluid interface undergoing Rayleigh-Taylor instability,an example of bubble ascending dynamics,and a drop impacting on a free interface whose dynamics we compare with both existing numerical and experimental data.展开更多
The migration of deformable drops in the channel flow neglecting the gravity influence is investigated numerically by solving the incompressible Navier-Stokes equations using the finite- difference method coupled with...The migration of deformable drops in the channel flow neglecting the gravity influence is investigated numerically by solving the incompressible Navier-Stokes equations using the finite- difference method coupled with the front-tracking technique.The objectives of this study are to examine the effectiveness of the present approach for predicting the migration of drops in a shear flow and to investigate the behavior of the drop migration in the channel flow under zero-gravity.To validate the present calculation,some typical results are compared with available computational and theoretical data,which confirms that the present approach is reliable in predicting the drop migration. With respect to the drop migration in the channel flow at finite Reynolds numbers,the drops either move to an equilibrium lateral position or undergo an oscillatory motion under different conditions. The effects of some typical parameters,e.g.,the Reynolds number,the Weber number,the viscosity ratio and the density ratio of the drop fluid to the suspending medium,and the drop size,on the migration of drops are discussed and analyzed.展开更多
基金Project supported by the National Natural Science Foundation of China(No.10971132)the Shanghai Pujiang Program(No.[2006]118)
文摘This paper presents the numerical simulations of two Richtmyer-Meshkov （RM） instability experiments using the conservative front-tracking method developed in （Mao, D. Towards front-tracking based on conservation in two space dimensions II, tracking discontinuities in capturing fashion. J. Comput. Phys., 226, 1550-1588 （2007））. The numerical results are compared with those obtained in （Holmes, R. L., Grove, J. W., and Sharp, D. H. Numerical investigation of Richtmyer-Meshkov instability using front-tracking. J. Fluid Mech., 301, 51-64 （1995））. The present simulations are generally in good agreement with those obtained by Holmes et al., and also capture the nonlinear and compessive phenomenon, i.e., the self-interactions of the transmitted and reflected wave edges, which was pointed out by Holmes et al. as the cause of the deceleration of the interfaces. However, the perturbation amplitudes and the amplitude growth rates of the interfaces obtained with the present conservative front-tracking method are a bit larger than those obtained by Holmes et al.
基金supported by the National Natural Science Foundation of China(Grant No.11572062)the Fundamental Research Funds for the Central Universities,China(Grant No.CDJZR13248801)+2 种基金the Program for Changjiang Scholars and Innovative Research Team in University,China(Grant No.IRT13043)Key Laboratory of Functional Crystals and Laser Technology,TIPCChinese Academy of Sciences
文摘We developed a three-dimensional multi-relaxation-time lattice Boltzmann method for incompressible and immiscible two-phase flow by coupling with a front-tracking technique. The flow field was simulated by using an Eulerian grid, an adaptive unstructured triangular Lagrangian grid was applied to track explicitly the motion of the two-fluid interface, and an indicator function was introduced to update accurately the fluid properties. The surface tension was computed directly on a triangular Lagrangian grid, and then the surface tension was distributed to the background Eulerian grid. Three benchmarks of two-phase flow, including the Laplace law for a stationary drop, the oscillation of a three-dimensional ellipsoidal drop, and the drop deformation in a shear flow, were simulated to validate the present model.
基金Project supported by the National Natural Science Foundation of China (No.10171063)
文摘An approach to deal with movings and collisions of arbitrary many discontinuities in the conservative front tracking method is developed. Using this approach one may develop an ＂all-purposed and robust＂ front-tracking algorithm. The algorithm with this approach may have some inconsistency and thus will have 0（1） magnitude errors in some grid cells at sometimes. Nevertheless, these errors will be eliminated by the conservation-preserving property of the front-tracking method in the following computation. Numerical examples are presented to illustrate the efficiency of the approach.
基金supported in part by National Science Council of Taiwan under research grant NSC-97-2628-M-009-007-MY3 and MoE-ATU projectH.Huang is supported by grants from the Natural Science and Engineering Research Council(NSERC)of Canada and the Mathematics of Information Technology and Complex Systems(MI-TACS)of Canada。
文摘In this paper,we present a finite difference method to track a network of curves whose motion is determined by mean curvature.To study the effect of inhomogeneous surface tension on the evolution of the network of curves,we include surfactant which can diffuse along the curves.The governing equations consist of one parabolic equation for the curve motion coupled with a convection-diffusion equation for the surfactant concentration along each curve.Our numerical method is based on a direct discretization of the governing equations which conserves the total surfactant mass in the curve network.Numerical experiments are carried out to examine the effects of inhomogeneous surface tension on the motion of the network,including the von Neumann law for cell growth in two space dimensions.
基金provided by the National Science Foundation under Grant number DMS 0609996(HDC)by the Fundacao de Amparoa Pesquisa do Estado de Sao Paulo(FAPESP)under Grant numbers 04/13781-1 and 06/57099-5(AMR)the Conselho Nacional de Desenvolvimento Cientifico e Tecnologico(CNPq)under Grant number 155491/2006-7(MMV).
文摘We present a variable time step,fully adaptive in space,hybrid method for the accurate simulation of incompressible two-phase flows in the presence of surface tension in two dimensions.The method is based on the hybrid level set/front-tracking approach proposed in[H.D.Ceniceros and A.M.Roma,J.Comput.Phys.,205,391-400,2005].Geometric,interfacial quantities are computed from front-tracking via the immersed-boundary setting while the signed distance(level set)function,which is evaluated fast and to machine precision,is used as a fluid indicator.The surface tension force is obtained by employing the mixed Eulerian/Lagrangian representation introduced in[S.Shin,S.I.Abdel-Khalik,V.Daru and D.Juric,J.Comput.Phys.,203,493-516,2005]whose success for greatly reducing parasitic currents has been demonstrated.The use of our accurate fluid indicator together with effective Lagrangian marker control enhance this parasitic current reduction by several orders of magnitude.To resolve accurately and efficiently sharp gradients and salient flow features we employ dynamic,adaptive mesh refinements.This spatial adaption is used in concert with a dynamic control of the distribution of the Lagrangian nodes along the fluid interface and a variable time step,linearly implicit time integration scheme.We present numerical examples designed to test the capabilities and performance of the proposed approach as well as three applications:the long-time evolution of a fluid interface undergoing Rayleigh-Taylor instability,an example of bubble ascending dynamics,and a drop impacting on a free interface whose dynamics we compare with both existing numerical and experimental data.
基金The project supported by the National Natural Science Foundation of China (10125210) and the Hundred-Talent Programme of the Chinese Academy of Sciences
文摘The migration of deformable drops in the channel flow neglecting the gravity influence is investigated numerically by solving the incompressible Navier-Stokes equations using the finite- difference method coupled with the front-tracking technique.The objectives of this study are to examine the effectiveness of the present approach for predicting the migration of drops in a shear flow and to investigate the behavior of the drop migration in the channel flow under zero-gravity.To validate the present calculation,some typical results are compared with available computational and theoretical data,which confirms that the present approach is reliable in predicting the drop migration. With respect to the drop migration in the channel flow at finite Reynolds numbers,the drops either move to an equilibrium lateral position or undergo an oscillatory motion under different conditions. The effects of some typical parameters,e.g.,the Reynolds number,the Weber number,the viscosity ratio and the density ratio of the drop fluid to the suspending medium,and the drop size,on the migration of drops are discussed and analyzed.
