In this work, two-grid characteristic finite volume schemes for the nonlinear parabolic problem are considered. In our algorithms, the diffusion term is discretized by the finite volume method, while the temporal diff...In this work, two-grid characteristic finite volume schemes for the nonlinear parabolic problem are considered. In our algorithms, the diffusion term is discretized by the finite volume method, while the temporal differentiation and advection terms are treated by the characteristic scheme. Under some conditions about the coefficients and exact solution, optimal error estimates for the numerical solution are obtained. Furthermore, the two- grid characteristic finite volume methods involve solving a nonlinear equation on coarse mesh with mesh size H, a large linear problem for the Oseen two-grid characteristic finite volume method on a fine mesh with mesh size h = O（H2） or a large linear problem for the Newton two-grid characteristic finite volume method on a fine mesh with mesh size h = 0（I log hll/2H3）. These methods we studied provide the same convergence rate as that of the characteristic finite volume method, which involves solving one large nonlinear problem on a fine mesh with mesh size h. Some numerical results are presented to demonstrate the efficiency of the proposed methods.展开更多
A time domain finite volume method（TDFVM）based on wave theory is developed to analyze the transient response and natural characteristics of structural-acoustic coupling problems in an enclosed cavity.In the present ...A time domain finite volume method（TDFVM）based on wave theory is developed to analyze the transient response and natural characteristics of structural-acoustic coupling problems in an enclosed cavity.In the present method,the elastic dynamic equations and acoustic equation in heterogeneous medium are solved in solid domains and fluid domains respectively.The structural-acoustic coupling is implemented according to the continuity condition of the particle velocity along the normal direction and the normal traction equilibrium condition on the interface.Several numerical examples are presented to validate the effectiveness and accuracy of the present TDFVM.Then the effects of water depth on the acoustic and vibration characteristics and the natural characteristics of a structural-acoustic coupling system are analyzed.The numerical results show that the increase of water depth leads to a stronger coupling between the water and structure and the decrease of natural frequencies of coupling system,The computational cost and memory of this method are small and it can be applicable to structural-acoustic coupling problems in the heterogeneous fluid.展开更多
Offshore observation platforms are required to have great ability to resist waves when they are operating at sea. Investigation on the motion characteristics of the platforms in the sea can provide significant referen...Offshore observation platforms are required to have great ability to resist waves when they are operating at sea. Investigation on the motion characteristics of the platforms in the sea can provide significant reference values during the platform design procedure. In this paper, a series of numerical simulation on the interaction of a triple-hulled offshore observation platform with different incident waves is carried out. All of the simulations are implemented utilizing our own solver naoe-FOAM-SJTU, which is based and developed on the open source tools of OpenFOAM. Duration curves of motion characteristics and loads acting on the platform are obtained, and a comparison between the results of the amplitude in different incident waves is presented. The results show that the solver is competent in the simulation of motion response of platforms in waves.展开更多
基金Acknowledgments. The work was supported by the Natural Science Foundation of China （No.11126117）, CAPES and CNPq of Brazil, and the Doctor Fund of Henan Polytechnic Univer- sity （B2012-098）. The author is very grateful to Professor JinYun Yuan for his kind invitation to visit the Universidade Federal do Paran, Brazil.
文摘In this work, two-grid characteristic finite volume schemes for the nonlinear parabolic problem are considered. In our algorithms, the diffusion term is discretized by the finite volume method, while the temporal differentiation and advection terms are treated by the characteristic scheme. Under some conditions about the coefficients and exact solution, optimal error estimates for the numerical solution are obtained. Furthermore, the two- grid characteristic finite volume methods involve solving a nonlinear equation on coarse mesh with mesh size H, a large linear problem for the Oseen two-grid characteristic finite volume method on a fine mesh with mesh size h = O（H2） or a large linear problem for the Newton two-grid characteristic finite volume method on a fine mesh with mesh size h = 0（I log hll/2H3）. These methods we studied provide the same convergence rate as that of the characteristic finite volume method, which involves solving one large nonlinear problem on a fine mesh with mesh size h. Some numerical results are presented to demonstrate the efficiency of the proposed methods.
基金supported by the Fundamental Research Funds for the Central Universities(HEUCF100307)the National Natural Science Foundation of China(51279035)
文摘A time domain finite volume method（TDFVM）based on wave theory is developed to analyze the transient response and natural characteristics of structural-acoustic coupling problems in an enclosed cavity.In the present method,the elastic dynamic equations and acoustic equation in heterogeneous medium are solved in solid domains and fluid domains respectively.The structural-acoustic coupling is implemented according to the continuity condition of the particle velocity along the normal direction and the normal traction equilibrium condition on the interface.Several numerical examples are presented to validate the effectiveness and accuracy of the present TDFVM.Then the effects of water depth on the acoustic and vibration characteristics and the natural characteristics of a structural-acoustic coupling system are analyzed.The numerical results show that the increase of water depth leads to a stronger coupling between the water and structure and the decrease of natural frequencies of coupling system,The computational cost and memory of this method are small and it can be applicable to structural-acoustic coupling problems in the heterogeneous fluid.
基金Supported by the National Natural Science Foundation of China （Grant No. 50739004 and 11072154） Foundation of State Key Laboratory of Ocean Engineering of China （GKZD010059）+1 种基金 the Program for Professor of Special Appointment （Eastern Scholar） at Shanghai Institutions of Higher Learning （2008007） The Lloyd＇s Register Educational Trust （The LRET）
文摘Offshore observation platforms are required to have great ability to resist waves when they are operating at sea. Investigation on the motion characteristics of the platforms in the sea can provide significant reference values during the platform design procedure. In this paper, a series of numerical simulation on the interaction of a triple-hulled offshore observation platform with different incident waves is carried out. All of the simulations are implemented utilizing our own solver naoe-FOAM-SJTU, which is based and developed on the open source tools of OpenFOAM. Duration curves of motion characteristics and loads acting on the platform are obtained, and a comparison between the results of the amplitude in different incident waves is presented. The results show that the solver is competent in the simulation of motion response of platforms in waves.
