The scaled boundary finite element method(SBFEM) is a semi-analytical numerical method,which models an analysis domain by a small number of large-sized subdomains and discretises subdomain boundaries only.In a subdoma...The scaled boundary finite element method(SBFEM) is a semi-analytical numerical method,which models an analysis domain by a small number of large-sized subdomains and discretises subdomain boundaries only.In a subdomain,all fields of state variables including displacement,stress,velocity and acceleration are semi-analytical,and the kinetic energy,strain energy and energy error are all integrated semi-analytically.These advantages are taken in this study to develop a posteriori h-hierarchical adaptive SBFEM for transient elastodynamic problems using a mesh refinement procedure which subdivides subdomains.Because only a small number of subdomains are subdivided,mesh refinement is very simple and efficient,and mesh mapping to transfer state variables from an old mesh to a new one is also very simple but accurate.Two 2D examples with stress wave propagation were modelled.The results show that the developed method is capable of capturing propagation of steep stress regions and calculating accurate dynamic responses,using only a fraction of degrees of freedom required by adaptive finite element method.展开更多
The present study provides a three-dimensional volume-of-fluid method based on the adaptive mesh refinement technique.The projection method on the adaptive mesh is introduced for solving the incompressible Navier-Stok...The present study provides a three-dimensional volume-of-fluid method based on the adaptive mesh refinement technique.The projection method on the adaptive mesh is introduced for solving the incompressible Navier-Stokes equations.The octree structure mesh is employed to solve the flow velocities and the pressure.The developed solver is applied to simulate the deformation of the cubic droplet driven by the surface tension without the effect of the gravity.The numerical results well predict the shape evolution of the droplet.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
A novel CFD approach based on adaptive mesh refinement（AMR） technique is being developed for numerical simulation of violent free surface flows. CIP method is applied to the flow solver and tangent of hyperbola for ...A novel CFD approach based on adaptive mesh refinement（AMR） technique is being developed for numerical simulation of violent free surface flows. CIP method is applied to the flow solver and tangent of hyperbola for interface capturing with slope weighting（THINC/SW） scheme is implemented as the free surface capturing scheme. The PETSc library is adopted to solve the linear system. The linear solver is redesigned and modified to satisfy the requirement of the AMR mesh topology. In this paper, our CFD method is outlined and newly obtained results on numerical simulation of violent free surface flows are presented.展开更多
We consider the design of an effective and reliable adaptive finite element method(AFEM)for the nonlinear Poisson-Boltzmann equation(PBE).We first examine the two-term regularization technique for the continuous probl...We consider the design of an effective and reliable adaptive finite element method(AFEM)for the nonlinear Poisson-Boltzmann equation(PBE).We first examine the two-term regularization technique for the continuous problem recently proposed by Chen,Holst and Xu based on the removal of the singular electrostatic potential inside biomolecules;this technique made possible the development of the first complete solution and approximation theory for the Poisson-Boltzmann equation,the first provably convergent discretization and also allowed for the development of a provably convergent AFEM.However,in practical implementation,this two-term regularization exhibits numerical instability.Therefore,we examine a variation of this regularization technique which can be shown to be less susceptible to such instability.We establish a priori estimates and other basic results for the continuous regularized problem,as well as for Galerkin finite element approximations.We show that the new approach produces regularized continuous and discrete problemswith the samemathematical advantages of the original regularization.We then design an AFEM scheme for the new regularized problem and show that the resulting AFEM scheme is accurate and reliable,by proving a contraction result for the error.This result,which is one of the first results of this type for nonlinear elliptic problems,is based on using continuous and discrete a priori L¥estimates.To provide a high-quality geometric model as input to the AFEM algorithm,we also describe a class of feature-preserving adaptive mesh generation algorithms designed specifically for constructing meshes of biomolecular structures,based on the intrinsic local structure tensor of the molecular surface.All of the algorithms described in the article are implemented in the Finite Element Toolkit(FETK),developed and maintained at UCSD.The stability advantages of the new regularization scheme are demonstrated with FETK through comparisons with the original regularization approach for a model problem.The convergence and accuracy of the overall AFEMalgorithmis also illustrated by numerical approximation of electrostatic solvation energy for an insulin protein.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.50579081)EPSRC UK(Grant No.EP/F00656X/1)+1 种基金the State Key Laboratory of Water Resources and Hydropower Engineering Science,Wuhan University,China through an open Research (Grant No.2010A004)Zhang's one-year research visit to the University of Liv-erpool was funded by China Scholarship Council
文摘The scaled boundary finite element method(SBFEM) is a semi-analytical numerical method,which models an analysis domain by a small number of large-sized subdomains and discretises subdomain boundaries only.In a subdomain,all fields of state variables including displacement,stress,velocity and acceleration are semi-analytical,and the kinetic energy,strain energy and energy error are all integrated semi-analytically.These advantages are taken in this study to develop a posteriori h-hierarchical adaptive SBFEM for transient elastodynamic problems using a mesh refinement procedure which subdivides subdomains.Because only a small number of subdomains are subdivided,mesh refinement is very simple and efficient,and mesh mapping to transfer state variables from an old mesh to a new one is also very simple but accurate.Two 2D examples with stress wave propagation were modelled.The results show that the developed method is capable of capturing propagation of steep stress regions and calculating accurate dynamic responses,using only a fraction of degrees of freedom required by adaptive finite element method.
基金This work was supported by the National Natural Science Foun-dation of China(No.41776194).
文摘The present study provides a three-dimensional volume-of-fluid method based on the adaptive mesh refinement technique.The projection method on the adaptive mesh is introduced for solving the incompressible Navier-Stokes equations.The octree structure mesh is employed to solve the flow velocities and the pressure.The developed solver is applied to simulate the deformation of the cubic droplet driven by the surface tension without the effect of the gravity.The numerical results well predict the shape evolution of the droplet.
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.
文摘A novel CFD approach based on adaptive mesh refinement（AMR） technique is being developed for numerical simulation of violent free surface flows. CIP method is applied to the flow solver and tangent of hyperbola for interface capturing with slope weighting（THINC/SW） scheme is implemented as the free surface capturing scheme. The PETSc library is adopted to solve the linear system. The linear solver is redesigned and modified to satisfy the requirement of the AMR mesh topology. In this paper, our CFD method is outlined and newly obtained results on numerical simulation of violent free surface flows are presented.
基金supported in part by NSF Awards 0715146,0821816,0915220 and 0822283(CTBP)NIHAward P41RR08605-16(NBCR),DOD/DTRA Award HDTRA-09-1-0036+1 种基金CTBP,NBCR,NSF and NIHsupported in part by NIH,NSF,HHMI,CTBP and NBCR.The third,fourth and fifth authors were supported in part by NSF Award 0715146,CTBP,NBCR and HHMI.
文摘We consider the design of an effective and reliable adaptive finite element method(AFEM)for the nonlinear Poisson-Boltzmann equation(PBE).We first examine the two-term regularization technique for the continuous problem recently proposed by Chen,Holst and Xu based on the removal of the singular electrostatic potential inside biomolecules;this technique made possible the development of the first complete solution and approximation theory for the Poisson-Boltzmann equation,the first provably convergent discretization and also allowed for the development of a provably convergent AFEM.However,in practical implementation,this two-term regularization exhibits numerical instability.Therefore,we examine a variation of this regularization technique which can be shown to be less susceptible to such instability.We establish a priori estimates and other basic results for the continuous regularized problem,as well as for Galerkin finite element approximations.We show that the new approach produces regularized continuous and discrete problemswith the samemathematical advantages of the original regularization.We then design an AFEM scheme for the new regularized problem and show that the resulting AFEM scheme is accurate and reliable,by proving a contraction result for the error.This result,which is one of the first results of this type for nonlinear elliptic problems,is based on using continuous and discrete a priori L¥estimates.To provide a high-quality geometric model as input to the AFEM algorithm,we also describe a class of feature-preserving adaptive mesh generation algorithms designed specifically for constructing meshes of biomolecular structures,based on the intrinsic local structure tensor of the molecular surface.All of the algorithms described in the article are implemented in the Finite Element Toolkit(FETK),developed and maintained at UCSD.The stability advantages of the new regularization scheme are demonstrated with FETK through comparisons with the original regularization approach for a model problem.The convergence and accuracy of the overall AFEMalgorithmis also illustrated by numerical approximation of electrostatic solvation energy for an insulin protein.
