It is difficult to compute far-field waves in a relative large area by using one wave generation model when a large calculation domain is needed because of large dimensions of the waterway and long distance of the req...It is difficult to compute far-field waves in a relative large area by using one wave generation model when a large calculation domain is needed because of large dimensions of the waterway and long distance of the required computing points. Variation of waterway bathymetry and nonlinearity in the far field cannot be included in a ship fixed process either. A coupled method combining a wave generation model and wave propagation model is then used in this paper to simulate the wash waves generated by the passing ship. A NURBS-based higher order panel method is adopted as the stationary wave generation model; a wave spectrum method and Boussinesq-type equation wave model are used as the wave propagation model for the constant water depth condition and variable water depth condition, respectively. The waves calculated by the NURBS-based higher order panel method in the near field are used as the input for the wave spectrum method and the Boussinesq-type equation wave model to obtain the far-field waves. With this approach it is possible to simulate the ship wash waves including the effects of water depth and waterway bathymetry. Parts of the calculated results are validated experimentally, and the agreement is demonstrated. The effects of ship wash waves on the moored ship are discussed by using a diffraction theory method. The results indicate that the prediction of the ship induced waves by coupling models is feasible.展开更多
In this paper the wave equation model (WEM) [1] is extended to solve advection-dominant heat transfer problems in multi-dimensional space. Based on the operator-splitting method the heat transfer equation is divided i...In this paper the wave equation model (WEM) [1] is extended to solve advection-dominant heat transfer problems in multi-dimensional space. Based on the operator-splitting method the heat transfer equation is divided into an advection equation and a diffusion equation which are solved separately. In advection stage the first order advection equation is transferred to a second order wave equation first, than the wave equation is solved by FEM with mass lumping. The diffusion equation can be solved accurately without many difficulties. A number of numerical examples of multi-dimensional advection are presented in which the advection velocities are non-uniform in space and unsteady in time. The numerical results are quite accurate in comparison with the exact solutions.The mass lumping saves computational effort greatly.展开更多
Wave equation model (WEM) first developed by Lynch and Gray [2] is one of accurate and effective numerical methods to resolve shallow water equations. This paper shows the numerical consistency of the second-order wav...Wave equation model (WEM) first developed by Lynch and Gray [2] is one of accurate and effective numerical methods to resolve shallow water equations. This paper shows the numerical consistency of the second-order wave equation and the first-order continuity equation, analyzes the error between them. This paper also shows that the numerical friction factor τ0 appearing in wave equation is of key importance to the numerical solutions and mass conservation of wave equation model. Numerical calculations of M2 tidal waves in rectangular harbor and a quarter annular harbor are made to demonstrate that it is possible to find a proper numerical friction factor To with which accurate solutions and satisfactory mass conservation can be achieved by wave equation model.展开更多
In this paper, three types of nonlinear evolution equations such as (2n + 1)th order KdV equation, etc, are studied. And their solitary wave solutions of rational form obtained are available and possess the simplest f...In this paper, three types of nonlinear evolution equations such as (2n + 1)th order KdV equation, etc, are studied. And their solitary wave solutions of rational form obtained are available and possess the simplest form so far. At last, the Hamiltonian form of (2n + 1)th order general KdV equation is generalized.展开更多
This paper employs finite element method to solve shallow water equations with absorbing boundary conditions(the third kind,mixed boundary conditions).It is of practical importance in the cases that the land boundarie...This paper employs finite element method to solve shallow water equations with absorbing boundary conditions(the third kind,mixed boundary conditions).It is of practical importance in the cases that the land boundaries of the coastal area are made of porous medium allowing sea water flow in or out.The absorbing boundary conditions are treated as natural boundary conditions in wave equation finite element model.The numerical results for rectangu- lar and quarterly annular harbors indicate that the numerical solutions agree very well with ana- lytic solutions,which are also given in this paper.It is found that the land boundary absorbabili- ty may be significant to long wave oscillations,such as tidal waves in coastal harbors.展开更多
基金financially supported by the National Natural Science Foundation of China(Grant Nos.50879066 and 51409201)the Research Fund for the Doctoral Program of Higher Education of China(Grant No.200804970009)
文摘It is difficult to compute far-field waves in a relative large area by using one wave generation model when a large calculation domain is needed because of large dimensions of the waterway and long distance of the required computing points. Variation of waterway bathymetry and nonlinearity in the far field cannot be included in a ship fixed process either. A coupled method combining a wave generation model and wave propagation model is then used in this paper to simulate the wash waves generated by the passing ship. A NURBS-based higher order panel method is adopted as the stationary wave generation model; a wave spectrum method and Boussinesq-type equation wave model are used as the wave propagation model for the constant water depth condition and variable water depth condition, respectively. The waves calculated by the NURBS-based higher order panel method in the near field are used as the input for the wave spectrum method and the Boussinesq-type equation wave model to obtain the far-field waves. With this approach it is possible to simulate the ship wash waves including the effects of water depth and waterway bathymetry. Parts of the calculated results are validated experimentally, and the agreement is demonstrated. The effects of ship wash waves on the moored ship are discussed by using a diffraction theory method. The results indicate that the prediction of the ship induced waves by coupling models is feasible.
文摘In this paper the wave equation model (WEM) [1] is extended to solve advection-dominant heat transfer problems in multi-dimensional space. Based on the operator-splitting method the heat transfer equation is divided into an advection equation and a diffusion equation which are solved separately. In advection stage the first order advection equation is transferred to a second order wave equation first, than the wave equation is solved by FEM with mass lumping. The diffusion equation can be solved accurately without many difficulties. A number of numerical examples of multi-dimensional advection are presented in which the advection velocities are non-uniform in space and unsteady in time. The numerical results are quite accurate in comparison with the exact solutions.The mass lumping saves computational effort greatly.
文摘Wave equation model (WEM) first developed by Lynch and Gray [2] is one of accurate and effective numerical methods to resolve shallow water equations. This paper shows the numerical consistency of the second-order wave equation and the first-order continuity equation, analyzes the error between them. This paper also shows that the numerical friction factor τ0 appearing in wave equation is of key importance to the numerical solutions and mass conservation of wave equation model. Numerical calculations of M2 tidal waves in rectangular harbor and a quarter annular harbor are made to demonstrate that it is possible to find a proper numerical friction factor To with which accurate solutions and satisfactory mass conservation can be achieved by wave equation model.
文摘In this paper, three types of nonlinear evolution equations such as (2n + 1)th order KdV equation, etc, are studied. And their solitary wave solutions of rational form obtained are available and possess the simplest form so far. At last, the Hamiltonian form of (2n + 1)th order general KdV equation is generalized.
文摘This paper employs finite element method to solve shallow water equations with absorbing boundary conditions(the third kind,mixed boundary conditions).It is of practical importance in the cases that the land boundaries of the coastal area are made of porous medium allowing sea water flow in or out.The absorbing boundary conditions are treated as natural boundary conditions in wave equation finite element model.The numerical results for rectangu- lar and quarterly annular harbors indicate that the numerical solutions agree very well with ana- lytic solutions,which are also given in this paper.It is found that the land boundary absorbabili- ty may be significant to long wave oscillations,such as tidal waves in coastal harbors.
