Very Large Floating Structures (VLFS) have drawn considerable attention recently due to their potential significance in the exploitation of ocean resources and in the utilization of ocean space. Efficient and accurate...Very Large Floating Structures (VLFS) have drawn considerable attention recently due to their potential significance in the exploitation of ocean resources and in the utilization of ocean space. Efficient and accurate estimation of their hydroelastic responses to waves is very important for the design. Recently, an efficient numerical algorithm was developed by Ertekin and Kim (1999). However, in their analysis, the linear Level I Green-Naghdi (GN) theory is employed to describe fluid dynamics instead of the conventional linear wave (LW) theory of finite water depth. They claimed that this linear level I GN theory provided better predictions of the hydroelastic responses of VLFS than the linear wave theory. In this paper, a detailed derivation is given in the conventional linear wave theory framework with the same quantity as used in the linear level I GN theory framework. This allows a critical comparison between the linear wave theory and the linear level I GN theory. It is found that the linear level I GN theory can be regarded as an approximation to the linear wave theory of finite water depth. The consequences of the differences between these two theories in the predicted hydroelastic responses are studied quantitatively. And it is found that the linear level I GN theory is not superior to the linear wave theory. Finally, various factors affecting the hydroelastic response of VLFS are studied with the implemented algorithm.展开更多
“Green–Naghdi Theory,Part A:Green–Naghdi(GN)Equations for Shallow Water Waves”have investigated the linear dispersion relations of high-level GN equations in shallow water.In this study,the GN equations for deep w...“Green–Naghdi Theory,Part A:Green–Naghdi(GN)Equations for Shallow Water Waves”have investigated the linear dispersion relations of high-level GN equations in shallow water.In this study,the GN equations for deep water waves are investigated.In the traditional GN equations for deep water waves,the velocity distribution assumption involves only one representative wave number.Herein,a new velocity distribution shape function with multiple representative wave numbers is employed.Further,we have derived the three-dimensional GN equations and analyzed the linear dispersion relations of the GN-3 and GN-5 equations.In this study,the finite difference method is used to simulate focus waves in the time domain.Additionally,the GN-5 equations are used to validate the wave profile and horizontal velocity distribution along water depth for different focused waves.展开更多
A numerical scheme based on hybrid central finite-volume and finite-difference method is presented to model Green-Naghdi water wave equations. The governing equations are reformulated into the conservative form, and t...A numerical scheme based on hybrid central finite-volume and finite-difference method is presented to model Green-Naghdi water wave equations. The governing equations are reformulated into the conservative form, and the convective flux is estimated using a Godunov-type finite volume method while the remaining terms are discretized using finite difference method. To enhance the robustness of the model, a central-upwind flux evaluation and a well-balanced non- negative water depth construction are incorporated. Numerical tests demonstrate that present model has the advantages of stability preserving and numerical efficiency.展开更多
We consider the stabilization of Naghdis model by boundary feedbacks wherethe model has a middle surface of any shape. First, applying the semigroup approach and theregularity of elliptic boundary value problems, we o...We consider the stabilization of Naghdis model by boundary feedbacks wherethe model has a middle surface of any shape. First, applying the semigroup approach and theregularity of elliptic boundary value problems, we obtain the existence, the uniqueness, and theproperties of solutions to Naghdis model. Finally, we establish the exponential decay rates forNaghdis model under some checkable geometric conditions on the middle surface.展开更多
The thermoelastic diffusion problem of an isotropic half-space is presented.The Green-Naghdi model with and without energy dissipation is proposed.Novel multi single/dual-phase-lag models are presented to investigate ...The thermoelastic diffusion problem of an isotropic half-space is presented.The Green-Naghdi model with and without energy dissipation is proposed.Novel multi single/dual-phase-lag models are presented to investigate the thermoelastic diffusion behavior of the medium.The simple Green-Naghdi type Ⅱ and Ⅲ and their modified models are all examined here.The exact solution of thermodiffusion governing equations has been obtained considering the initial and boundary conditions.The validity of results is acceptable by comparing all variables.Benchmark results are reported to help other investigators in their future comparisons.展开更多
基金Supported by the Natural Science Foundation of Zhanjiang Normal University(L1104 and LZL1101)the Natural Science Foundation of Guangdong Province(S2013010015957)
基金by the National Natural Science Foundation of China(50039010)the Science and Technology Development Foundation of Shanghai Municipal Government(00XD14015)
文摘Very Large Floating Structures (VLFS) have drawn considerable attention recently due to their potential significance in the exploitation of ocean resources and in the utilization of ocean space. Efficient and accurate estimation of their hydroelastic responses to waves is very important for the design. Recently, an efficient numerical algorithm was developed by Ertekin and Kim (1999). However, in their analysis, the linear Level I Green-Naghdi (GN) theory is employed to describe fluid dynamics instead of the conventional linear wave (LW) theory of finite water depth. They claimed that this linear level I GN theory provided better predictions of the hydroelastic responses of VLFS than the linear wave theory. In this paper, a detailed derivation is given in the conventional linear wave theory framework with the same quantity as used in the linear level I GN theory framework. This allows a critical comparison between the linear wave theory and the linear level I GN theory. It is found that the linear level I GN theory can be regarded as an approximation to the linear wave theory of finite water depth. The consequences of the differences between these two theories in the predicted hydroelastic responses are studied quantitatively. And it is found that the linear level I GN theory is not superior to the linear wave theory. Finally, various factors affecting the hydroelastic response of VLFS are studied with the implemented algorithm.
文摘“Green–Naghdi Theory,Part A:Green–Naghdi(GN)Equations for Shallow Water Waves”have investigated the linear dispersion relations of high-level GN equations in shallow water.In this study,the GN equations for deep water waves are investigated.In the traditional GN equations for deep water waves,the velocity distribution assumption involves only one representative wave number.Herein,a new velocity distribution shape function with multiple representative wave numbers is employed.Further,we have derived the three-dimensional GN equations and analyzed the linear dispersion relations of the GN-3 and GN-5 equations.In this study,the finite difference method is used to simulate focus waves in the time domain.Additionally,the GN-5 equations are used to validate the wave profile and horizontal velocity distribution along water depth for different focused waves.
文摘A numerical scheme based on hybrid central finite-volume and finite-difference method is presented to model Green-Naghdi water wave equations. The governing equations are reformulated into the conservative form, and the convective flux is estimated using a Godunov-type finite volume method while the remaining terms are discretized using finite difference method. To enhance the robustness of the model, a central-upwind flux evaluation and a well-balanced non- negative water depth construction are incorporated. Numerical tests demonstrate that present model has the advantages of stability preserving and numerical efficiency.
基金This work is supported by the Mathematical Tianyuan Foundation of China(A0324641)Youth Science Foundation of Shanxi Province,China(20041001)
文摘We consider the stabilization of Naghdis model by boundary feedbacks wherethe model has a middle surface of any shape. First, applying the semigroup approach and theregularity of elliptic boundary value problems, we obtain the existence, the uniqueness, and theproperties of solutions to Naghdis model. Finally, we establish the exponential decay rates forNaghdis model under some checkable geometric conditions on the middle surface.
文摘The thermoelastic diffusion problem of an isotropic half-space is presented.The Green-Naghdi model with and without energy dissipation is proposed.Novel multi single/dual-phase-lag models are presented to investigate the thermoelastic diffusion behavior of the medium.The simple Green-Naghdi type Ⅱ and Ⅲ and their modified models are all examined here.The exact solution of thermodiffusion governing equations has been obtained considering the initial and boundary conditions.The validity of results is acceptable by comparing all variables.Benchmark results are reported to help other investigators in their future comparisons.
基金This work was supported by the National Natural Science Foundation of China(Grant No.11802242)the Fundamental Research Funds for the Central Universities(Grant No.D5000230066).
