Computation of potential flow around three-dimensional obstacles by a scaled boundary finite-element method

The scaled boundary finite-element method is a novel semi-analytical technique for solving the linear partial differential equation.The method discretizes the governing equation only on the boundary of the computational domain.Comparing with the finite-element method,the method reduces the spatial dimension by one,and the analytical procedure is applied at the reduced direction instead.Comparing with the boundary element method,the scaled boundary finite-element needs not the fundamental solution and thus no singular integrals must be evaluated.So the scaled boundary finite-element combines the advantages of the finite-element method and the boundary element method.A numerical model of the scaled boundary finite-element method is established to solve the three-dimensional Laplace equation in this paper,and further the flow around an obstacle is computed by this method.The numerical solutions are compared to the analytical ones and those from a boundary element method.The comparisons show that the present method can well simulate the flow field,and its accuracy is high.