The Application Of Scaled Boundary Finite Element Method In Potential Flow Theory

In the field of computational fluid dynamics,there are many numerical simulation methods,such as the finite difference method,the finite element method,the boundary element method,the finite volume method,etc.Recently,some new methods have been used in this field,such as particle method.The scaled boundary element finite element method is a novel method,which combines the advantages of the finite element and the boundary element methods,and this method was used in the structural mechanics firstly.A new coordinate system including the circumferential local co-ordinate and the radial co-ordinate has been established in the scaled boundary element finite element method.Only the boundary of the computational domain needs to be discretized in the circumferential direction as the same as the boundary element method.The solution in the radial direction is analytical,so the simulation precision of this method is high.This method can meet the infinity of the boundary condition automatically.The scaled boundary element finite element method is the finite element method which is discredited on the boundary of the computational domain,and it has a wide range of applications in the field of numerical simulation.In this paper the potential flow problems have been simulated using the scaled boundary element finite element method,including the potential flow in bounded domain and unbounded domain,the 2D or 3D wave action on structures and the water sloshing in 2D or 3D containers.Firstly the Laplace equation has been solved with the scaled boundary element finite element method for the potential flow problems.The derivative and solution process have been given for both the bounded domain and the unbounded domain problems,and the location of the scaled center has been discussed.For the problem wave action on 2D structures,the wave action on a fixed box on the free surface has been simulated using this method.The derivative and solution process have been given for both bound domain problems and unbound domain problems,and the simulation results have been compared with the analytic solution and the results from a boundary element method.The accuracy and the efficiency have been confirmed.Then the effect of the selection of grid and the distance of the computational domain has been discussed.This method can be used in solving the wave interaction with various forms of structure,such as submerged breakwaters,barrier breakwaters and so on,by changing the position of scaled center in bound domain.The wave action with structures for different sizes has been simulated,and the changing characters of the simulation results have been given.Through comparing with the analytic solution,the results from other numerical methods and experimental results,the accuracy and efficiency of this method have been testified.The water sloshing in 2D containers is studied by the scaled boundary finite element method.The usual method is to set the scaled center on the water surface for this problem, which results the calculation complicately.By changing the proportion of the scaled center, the solution process has been simplified,and the accuracy of simulation has been improved. Then the water sloshing in 2D Semi-circular and rectangular containers is studied,and the distribution of velocity potential and velocity has been given,which agree well with the analytical solutions.At last the 3D water sloshing problem is studied.The derivative and solution process of the scaled boundary finite element method have been derived in detail. The liner element and the high order element have been used in the simulation.Through comparison with the 2D analytical solution,it is found that the simulation with the high order element has a higher precision.The cylindrical container has also been computed,and the simulation results are agree with the analytical solution well.Finally,the scaled boundary finite element method has been coupled with the eigenfunction expansion method to simulate the wave reaction with structure problem.For the 2D problem,the scaled boundary finite element method is used in the bounded domain and the eigenfunction expansion method is used in the unbounded domain,and coupling on the junction.This method has higher precision and efficiency.For the 3D problem,the wave reaction with cylinder has been simulated,and the accuracy and efficiency of this method have been testified through the comparison with the analytic solutions.