A novel numerical method for eliminating the singular integral and boundary effect is processed. In the proposed method, the virtual boundaries corresponding to the numbers of the true boundary arguments are chosen to...A novel numerical method for eliminating the singular integral and boundary effect is processed. In the proposed method, the virtual boundaries corresponding to the numbers of the true boundary arguments are chosen to be as simple as possible. An indirect radial basis function network （IRBFN） constructed by functions resulting from the indeterminate integral is used to construct the approaching virtual source functions distributed along the virtual boundaries. By using the linear superposition method, the governing equations presented in the boundaries integral equations （BIE） can be established while the fundamental solutions to the problems are introduced. The singular value decomposition （SVD） method is used to solve the governing equations since an optimal solution in the least squares sense to the system equations is available. In addition, no elements are required, and the boundary conditions can be imposed easily because of the Kronecker delta function properties of the approaching functions. Three classical 2D elasticity problems have been examined to verify the performance of the method proposed. The results show that this method has faster convergence and higher accuracy than the conventional boundary type numerical methods.展开更多
The boundary knot method （BKM） is a truly meshless boundary-type radial basis function （RBF） collocation scheme, where the general solution is employed instead of the fundamental solution to avoid the fictitious o...The boundary knot method （BKM） is a truly meshless boundary-type radial basis function （RBF） collocation scheme, where the general solution is employed instead of the fundamental solution to avoid the fictitious outside boundary of the physical domain of interest. In this study, the BKM is first used to calculate the free vibration of free and simply-upported thin plates. Compared with the analytical solution and ANSYS （a commercial FEM code） results, the present BKM is highly accurate and fast convergent.展开更多
In practical fluid dynamic simulations, the bou n dary condition should be treated carefully because it always has crucial influen ce on the numerical accuracy, stability and efficiency. Two types of boundary tr eatme...In practical fluid dynamic simulations, the bou n dary condition should be treated carefully because it always has crucial influen ce on the numerical accuracy, stability and efficiency. Two types of boundary tr eatment methods for lattice Boltzmann method (LBM) are proposed. One is for the treatment of boundaries situated at lattice nodes, and the other is for the appr oximation of boundaries that are not located at the regular lattice nodes. The f irst type of boundary treatment method can deal with various dynamic boundaries on complex geometries by using a general set of formulas, which can maintain sec ond\|order accuracy. Based on the fact that the fluid flows simulated by LBM are not far from equilibrium, the unknown distributions at a boundary node are expr essed as the analogous forms of their corresponding equilibrium distributions. T herefore, the number of unknowns can be reduced and an always\|closed set of equ ations can be obtained for the solutions to pressure, velocity and special bound ary conditions on various geometries. The second type of boundary treatment is a complete interpolation scheme to treat curved boundaries. It comes from careful analysis of the relations between distribution functions at boundary nodes and their neighboring lattice nodes. It is stable for all situations and of second\| order accuracy. Basic ideas, implementation procedures and verifications with ty pical examples for the both treatments are presented. Numerical simulations and analyses show that they are accurate, stable, general and efficient for practica l simulations.展开更多
文摘A novel numerical method for eliminating the singular integral and boundary effect is processed. In the proposed method, the virtual boundaries corresponding to the numbers of the true boundary arguments are chosen to be as simple as possible. An indirect radial basis function network （IRBFN） constructed by functions resulting from the indeterminate integral is used to construct the approaching virtual source functions distributed along the virtual boundaries. By using the linear superposition method, the governing equations presented in the boundaries integral equations （BIE） can be established while the fundamental solutions to the problems are introduced. The singular value decomposition （SVD） method is used to solve the governing equations since an optimal solution in the least squares sense to the system equations is available. In addition, no elements are required, and the boundary conditions can be imposed easily because of the Kronecker delta function properties of the approaching functions. Three classical 2D elasticity problems have been examined to verify the performance of the method proposed. The results show that this method has faster convergence and higher accuracy than the conventional boundary type numerical methods.
基金supported by the National Natural Science Foundation of China(No.10672051).
文摘The boundary knot method （BKM） is a truly meshless boundary-type radial basis function （RBF） collocation scheme, where the general solution is employed instead of the fundamental solution to avoid the fictitious outside boundary of the physical domain of interest. In this study, the BKM is first used to calculate the free vibration of free and simply-upported thin plates. Compared with the analytical solution and ANSYS （a commercial FEM code） results, the present BKM is highly accurate and fast convergent.
文摘In practical fluid dynamic simulations, the bou n dary condition should be treated carefully because it always has crucial influen ce on the numerical accuracy, stability and efficiency. Two types of boundary tr eatment methods for lattice Boltzmann method (LBM) are proposed. One is for the treatment of boundaries situated at lattice nodes, and the other is for the appr oximation of boundaries that are not located at the regular lattice nodes. The f irst type of boundary treatment method can deal with various dynamic boundaries on complex geometries by using a general set of formulas, which can maintain sec ond\|order accuracy. Based on the fact that the fluid flows simulated by LBM are not far from equilibrium, the unknown distributions at a boundary node are expr essed as the analogous forms of their corresponding equilibrium distributions. T herefore, the number of unknowns can be reduced and an always\|closed set of equ ations can be obtained for the solutions to pressure, velocity and special bound ary conditions on various geometries. The second type of boundary treatment is a complete interpolation scheme to treat curved boundaries. It comes from careful analysis of the relations between distribution functions at boundary nodes and their neighboring lattice nodes. It is stable for all situations and of second\| order accuracy. Basic ideas, implementation procedures and verifications with ty pical examples for the both treatments are presented. Numerical simulations and analyses show that they are accurate, stable, general and efficient for practica l simulations.
