In this paper,a meshless regularization method of fundamental solutions is proposed for a two-dimensional,two-phase linear inverse Stefan problem.The numerical implementation and analysis are challenging since one nee...In this paper,a meshless regularization method of fundamental solutions is proposed for a two-dimensional,two-phase linear inverse Stefan problem.The numerical implementation and analysis are challenging since one needs to handle composite materials in higher dimensions.Furthermore,the inverse Stefan problem is ill-posed since small errors in the input data cause large errors in the desired output solution.Therefore,regularization is necessary in order to obtain a stable solution.Numerical results for several benchmark test examples are presented and discussed.展开更多
We consider an inverse heat conduction problem with variable coefficient on an annulus domain.In many practice applications,we cannot know the initial temperature during heat process,therefore we consider a non-charac...We consider an inverse heat conduction problem with variable coefficient on an annulus domain.In many practice applications,we cannot know the initial temperature during heat process,therefore we consider a non-characteristic Cauchy problem for the heat equation.The method of fundamental solutions is applied to solve this problem.Due to ill-posedness of this problem,we first discretize the problem and then regularize it in the form of discrete equation.Numerical tests are conducted for showing the effectiveness of the proposed method.展开更多
A novel panel-free approach based on the method of fundamental solutions (MFS) is proposed to solve the potential flow for predicting ship motion responses in the frequency domain according to strip theory. Compared w...A novel panel-free approach based on the method of fundamental solutions (MFS) is proposed to solve the potential flow for predicting ship motion responses in the frequency domain according to strip theory. Compared with the conventional boundary element method (BEM), MFS is a desingularized, panel-free and integration-free approach. As a result, it is mathematically simple and easy for programming. The velocity potential is described by radial basis function (RBF) approximations and any degree of continuity of the velocity potential gradient can be obtained. Desingularization is achieved through collating singularities on a pseudo boundary outside the real fluid domain. Practical implementation and numerical characteristics of the MFS for solving the potential flow problem concerning ship hydrodynamics are elaborated through the computation of a 2D rectangular section. Then, the current method is further integrated with frequency domain strip theory to predict the heave and pitch responses of a containership and a very large crude carrier (VLCC) in regular head waves. The results of both ships agree well with the 3D frequency domain panel method and experimental data. Thus, the correctness and usefulness of the proposed approach are proved. We hope that this paper will serve as a motivation for other researchers to apply the MFS to various challenging problems in the field of ship hydrodynamics.展开更多
The present work is concerned with a two-dimensional(2D)Stokes flow through a channel bounded by two parallel solid walls.The distance between the walls may be arbitrary,and the surface of one of the walls can be arbi...The present work is concerned with a two-dimensional(2D)Stokes flow through a channel bounded by two parallel solid walls.The distance between the walls may be arbitrary,and the surface of one of the walls can be arbitrarily rough.The main objective of this work consists in homogenizing the heterogeneous interface between the rough wall and fluid so as to obtain an equivalent smooth slippery fluid/solid interface characterized by an effective slip length.To solve the corresponding problem,two efficient numerical approaches are elaborated on the basis of the method of fundamental solution(MFS)and the boundary element methods(BEMs).They are applied to different cases where the fluid/solid interface is periodically or randomly rough.The results obtained by the proposed two methods are compared with those given by the finite element method and some relevant ones reported in the literature.This comparison shows that the two proposed methods are particularly efficient and accurate.展开更多
基金T.Reeve would like to acknowledge the financial support received from the EPSRC.
文摘In this paper,a meshless regularization method of fundamental solutions is proposed for a two-dimensional,two-phase linear inverse Stefan problem.The numerical implementation and analysis are challenging since one needs to handle composite materials in higher dimensions.Furthermore,the inverse Stefan problem is ill-posed since small errors in the input data cause large errors in the desired output solution.Therefore,regularization is necessary in order to obtain a stable solution.Numerical results for several benchmark test examples are presented and discussed.
基金partially supported by the Natural Science Foundation of Northwest Normal University,China(No.NWNU-LKQN-17-5).
文摘We consider an inverse heat conduction problem with variable coefficient on an annulus domain.In many practice applications,we cannot know the initial temperature during heat process,therefore we consider a non-characteristic Cauchy problem for the heat equation.The method of fundamental solutions is applied to solve this problem.Due to ill-posedness of this problem,we first discretize the problem and then regularize it in the form of discrete equation.Numerical tests are conducted for showing the effectiveness of the proposed method.
基金the Fund of the Minister of Education and Minister of Finance of China (No. ZXZY019)
文摘A novel panel-free approach based on the method of fundamental solutions (MFS) is proposed to solve the potential flow for predicting ship motion responses in the frequency domain according to strip theory. Compared with the conventional boundary element method (BEM), MFS is a desingularized, panel-free and integration-free approach. As a result, it is mathematically simple and easy for programming. The velocity potential is described by radial basis function (RBF) approximations and any degree of continuity of the velocity potential gradient can be obtained. Desingularization is achieved through collating singularities on a pseudo boundary outside the real fluid domain. Practical implementation and numerical characteristics of the MFS for solving the potential flow problem concerning ship hydrodynamics are elaborated through the computation of a 2D rectangular section. Then, the current method is further integrated with frequency domain strip theory to predict the heave and pitch responses of a containership and a very large crude carrier (VLCC) in regular head waves. The results of both ships agree well with the 3D frequency domain panel method and experimental data. Thus, the correctness and usefulness of the proposed approach are proved. We hope that this paper will serve as a motivation for other researchers to apply the MFS to various challenging problems in the field of ship hydrodynamics.
基金supported by the Vietnam National Foundation for Science and Technology Development(NAFOSTED)(No.107.02-2017.310)。
文摘The present work is concerned with a two-dimensional(2D)Stokes flow through a channel bounded by two parallel solid walls.The distance between the walls may be arbitrary,and the surface of one of the walls can be arbitrarily rough.The main objective of this work consists in homogenizing the heterogeneous interface between the rough wall and fluid so as to obtain an equivalent smooth slippery fluid/solid interface characterized by an effective slip length.To solve the corresponding problem,two efficient numerical approaches are elaborated on the basis of the method of fundamental solution(MFS)and the boundary element methods(BEMs).They are applied to different cases where the fluid/solid interface is periodically or randomly rough.The results obtained by the proposed two methods are compared with those given by the finite element method and some relevant ones reported in the literature.This comparison shows that the two proposed methods are particularly efficient and accurate.
