To reduce computational costs, an improved form of the frequency domain boundary element method（BEM） is proposed for two-dimensional radiation and propagation acoustic problems in a subsonic uniform flow with arbitr...To reduce computational costs, an improved form of the frequency domain boundary element method（BEM） is proposed for two-dimensional radiation and propagation acoustic problems in a subsonic uniform flow with arbitrary orientation. The boundary integral equation（BIE） representation solves the two-dimensional convected Helmholtz equation（CHE） and its fundamental solution, which must satisfy a new Sommerfeld radiation condition（SRC） in the physical space. In order to facilitate conventional formulations, the variables of the advanced form are expressed only in terms of the acoustic pressure as well as its normal and tangential derivatives, and their multiplication operators are based on the convected Green＇s kernel and its modified derivative. The proposed approach significantly reduces the CPU times of classical computational codes for modeling acoustic domains with arbitrary mean flow. It is validated by a comparison with the analytical solutions for the sound radiation problems of monopole,dipole and quadrupole sources in the presence of a subsonic uniform flow with arbitrary orientation.展开更多
Despite the significant number of boundary element method (BEM) solutions of time-dependent problems, certain concerns still need to be addressed. Foremost among these is the impact of different time discretization sc...Despite the significant number of boundary element method (BEM) solutions of time-dependent problems, certain concerns still need to be addressed. Foremost among these is the impact of different time discretization schemes on the accuracy of BEM modeling. Although very accurate for steady-state problems, the boundary element methods more often than not are computationally challenged when applied to transient problems. For the work reported herein, we investigate the level of accuracy achieved with different time-discretization schemes for the Green element method (GEM) solution of the unsteady convective transport equation. The Green element method (a modified BEM formulation) solves the boundary integral theory (A Fredholm integral equation of the second kind) on a generic element of the problem domain in a way that is typical of the finite element method (FEM). In this integration process a new system of discrete equations is produced which is banded and hence amenable to matrix manipulations. This is subsequently deployed to investigate the proper resolution in both space and time for the chosen transient 1D transport problems especially those involving shock wave propagation and different types of boundary conditions. It is found that for three out of the four numerical models developed in this study, the new system of discrete element equations generated for both space and temporal domains exhibits accurate characteristics even for cases involving advection-dominant transport. And for all the cases considered, the overall performance relies heavily on the temporal discretization scheme adopted.展开更多
本方法将板在特定域中的 Green 函数作为影响函数,首先根据连续板的外边界条件以及内支承条件建立方程,求出虚拟域中的 Green 函数“源”以及连续板的内支承反力,继而由求得的“源值”、内支承反力和板上的已知荷载确定板内任意点的挠...本方法将板在特定域中的 Green 函数作为影响函数,首先根据连续板的外边界条件以及内支承条件建立方程,求出虚拟域中的 Green 函数“源”以及连续板的内支承反力,继而由求得的“源值”、内支承反力和板上的已知荷载确定板内任意点的挠度和内力.方法简单,易于编程序,且未知量比边界元分域法进一步减少,适应性强,不受板的形状以及边界条件的限制。文中附若干算例,并将其数值结果与有限元法比较,表明本方法精度良好.展开更多
A new type of dual boundary integral equations(DBIE)is presented first,through which,a smaller system of equations needs to be solved in fracture analysis.Then a non-conforming crack tip element in two-dimensional pro...A new type of dual boundary integral equations(DBIE)is presented first,through which,a smaller system of equations needs to be solved in fracture analysis.Then a non-conforming crack tip element in two-dimensional problems is proposed.The exact formula for the hypersingular integral over the non-con- forming crack tip element is given next.By virtue of Green's-function-library strategy,a series of stress in- tensity factors(SIF)of different crack orientations,locations and/or sizes in a complicated structure can be obtained easily and efficiently.Finally,several examples of fracture analysis in two dimensions are given to demonstrate the accuracy and efficiency of the method proposed.展开更多
In this paper, we analyze the convergence of the adaptive conforming P 1 element method with the red-green refinement. Since the mesh after refining is not nested into the one before, the Galerkin-orthogonality does n...In this paper, we analyze the convergence of the adaptive conforming P 1 element method with the red-green refinement. Since the mesh after refining is not nested into the one before, the Galerkin-orthogonality does not hold for this case. To overcome such a difficulty, we prove some quasi-orthogonality instead under some mild condition on the initial mesh (Condition A). Consequently, we show convergence of the adaptive method by establishing the reduction of some total error. To weaken the condition on the initial mesh, we propose a modified red-green refinement and prove the convergence of the associated adaptive method under a much weaker condition on the initial mesh (Condition B).展开更多
基金supported by National Engineering School of Tunis (No.13039.1)
文摘To reduce computational costs, an improved form of the frequency domain boundary element method（BEM） is proposed for two-dimensional radiation and propagation acoustic problems in a subsonic uniform flow with arbitrary orientation. The boundary integral equation（BIE） representation solves the two-dimensional convected Helmholtz equation（CHE） and its fundamental solution, which must satisfy a new Sommerfeld radiation condition（SRC） in the physical space. In order to facilitate conventional formulations, the variables of the advanced form are expressed only in terms of the acoustic pressure as well as its normal and tangential derivatives, and their multiplication operators are based on the convected Green＇s kernel and its modified derivative. The proposed approach significantly reduces the CPU times of classical computational codes for modeling acoustic domains with arbitrary mean flow. It is validated by a comparison with the analytical solutions for the sound radiation problems of monopole,dipole and quadrupole sources in the presence of a subsonic uniform flow with arbitrary orientation.
文摘Despite the significant number of boundary element method (BEM) solutions of time-dependent problems, certain concerns still need to be addressed. Foremost among these is the impact of different time discretization schemes on the accuracy of BEM modeling. Although very accurate for steady-state problems, the boundary element methods more often than not are computationally challenged when applied to transient problems. For the work reported herein, we investigate the level of accuracy achieved with different time-discretization schemes for the Green element method (GEM) solution of the unsteady convective transport equation. The Green element method (a modified BEM formulation) solves the boundary integral theory (A Fredholm integral equation of the second kind) on a generic element of the problem domain in a way that is typical of the finite element method (FEM). In this integration process a new system of discrete equations is produced which is banded and hence amenable to matrix manipulations. This is subsequently deployed to investigate the proper resolution in both space and time for the chosen transient 1D transport problems especially those involving shock wave propagation and different types of boundary conditions. It is found that for three out of the four numerical models developed in this study, the new system of discrete element equations generated for both space and temporal domains exhibits accurate characteristics even for cases involving advection-dominant transport. And for all the cases considered, the overall performance relies heavily on the temporal discretization scheme adopted.
文摘本方法将板在特定域中的 Green 函数作为影响函数,首先根据连续板的外边界条件以及内支承条件建立方程,求出虚拟域中的 Green 函数“源”以及连续板的内支承反力,继而由求得的“源值”、内支承反力和板上的已知荷载确定板内任意点的挠度和内力.方法简单,易于编程序,且未知量比边界元分域法进一步减少,适应性强,不受板的形状以及边界条件的限制。文中附若干算例,并将其数值结果与有限元法比较,表明本方法精度良好.
基金the Aeronautical Science Foundation of China (No.99C53026).
文摘A new type of dual boundary integral equations(DBIE)is presented first,through which,a smaller system of equations needs to be solved in fracture analysis.Then a non-conforming crack tip element in two-dimensional problems is proposed.The exact formula for the hypersingular integral over the non-con- forming crack tip element is given next.By virtue of Green's-function-library strategy,a series of stress in- tensity factors(SIF)of different crack orientations,locations and/or sizes in a complicated structure can be obtained easily and efficiently.Finally,several examples of fracture analysis in two dimensions are given to demonstrate the accuracy and efficiency of the method proposed.
基金supported by National Natural Science Foundation of China (Grant Nos.10601003, 10971005)Foundation for the Author of National Excellent Doctoral Dissertation of China (Grant No.200718) National Basic Research Program of China (Grant No. 2005CB321704)
文摘In this paper, we analyze the convergence of the adaptive conforming P 1 element method with the red-green refinement. Since the mesh after refining is not nested into the one before, the Galerkin-orthogonality does not hold for this case. To overcome such a difficulty, we prove some quasi-orthogonality instead under some mild condition on the initial mesh (Condition A). Consequently, we show convergence of the adaptive method by establishing the reduction of some total error. To weaken the condition on the initial mesh, we propose a modified red-green refinement and prove the convergence of the associated adaptive method under a much weaker condition on the initial mesh (Condition B).
