A new finite element method, which is the characteristic-based operator-splitting (CBOS) algorithm, is developed to solve Navier-Stokes (N-S) equations. In each time step, the equations are split into the diffusive part and the convective part by adopting the operator-splitting algorithm. For the diffusive part, the temporal discretization is performed by the backward difference method which yields an implicit scheme and the spatial discretization is performed by the standard Galerkin method. The convective part can be discretized using the characteristic Galerkin method and solved explicitly. The driven square flow and backward-facing step flow are conducted to validate the model. It is shown that the numerical results agree well with the standard solutions or existing experimental data, and the present model has high accuracy and good stability. It provides a prospective research method for solving N-S equations.
A 3-D time-domain numerical coupled model is developed to obtain an efficient method for nonlinear waves acting on a box-shaped ship fixed in a harbor. The domain is divided into the inner domain and the outer domain. The inner domain is the area beneath the ship and the flow is described by the simplified Euler equations. The remaining area is the outer domain and the flow is defined by the higher-order Boussinesq equations in order to consider the nonlinearity of the wave motions. Along the interface boundaries between the inner domain and the outer domain, the volume flux is assumed to be continuous and the wave pressures are equal. Relevant physical experiment is conducted to validate the present mode/and it is shown that the numerical results agree with the experimental data. Compared the coupled model with the flow in the inner domain governed by the Laplace equation, the present coupled model is more efficient and its solution procedure is simpler, which is particularly useful for the study on the effect of the nonlinear waves acting on a fixed box-shaped ship in a large harbor.
