Efficient computation method for two-dimensional nonlinear waves

The theory and simulation of fully-nonlinear waves in a truncated two-dimensional wave tank in time domain are presented. A piston-type wave-maker is used to generate gravity waves into the tank field in finite water depth. A damping zone is added in front of the wave-maker which makes it become one kind of absorbing wave-maker and ensures the prescribed Neumann condition. The efficiency of numerical tank is further enhanced by installation of a sponge layer beach (SLB) in front of downtank to absorb longer weak waves that leak through the entire wave train front. Assume potential flow, the space- periodic irrotational surface waves can be represented by mixed Euler-lagrange particles Solving the integral equation at each time step for new normal velocities, the instantaneous free surface is integrated following time history by use of fourth-order Runge- Kutta method. The double node technique is used to deal with geometric discontinuity at the wave- body intersections. Several precise smoothing methods have been introduced to treat surface point with high curvature. No saw-tooth like instability is observed during the total simulation. The advantage of proposed wave tank has been verified by comparing with linear theoretical solution and other nonlinear results, excellent agreement in the whole range of frequencies of interest has been obtained.

Tests and Applications of An Approach to Absorbing Reflected Waves Towards Incident Boundary

If the upstream boundary conditions are prescribed based on the incident wave only, the time-dependent numerical models cannot effectively simulate the wave field when the physical or spurious reflected waves become significant. This paper describes carefully an approach to specifying the incident wave boundary conditions combined with a set sponge layer to absorb the reflected waves towards the incident boundary. Incorporated into a time-dependent numerical model, whose governing equations are the Boussinesq-type ones, the effectiveness of the approach is studied in detail. The general boundary conditions, describing the down-wave boundary conditions are also generalized to the case of random waves. The numerical model is in detail examined. The test cases include both the normal one-dimensional incident regular or random waves and the two-dimensional oblique incident regular waves. The calculated results show that the present approach is effective on damping the reflected waves towards the incident wave boundary.

An Efficient Hydrodynamic Model for Surface Waves

In the present study, a semi-implicit finite difference model for non-hydrostatic, free-surface flows is analyzed and discussed. The governing equations are the three-dimensional free-surface Reynolds-averaged Navier-Stokes equations defined on a general, irregular domain of arbitrary scale. At outflow, a combination of a sponge layer technique and a radiation boundary condition is applied to minimize wave reflection. The equations are solved with the fractional step method where the hydrostatic pressure component is determined first, while the non-hydrostatic component of the pressure is computed from the pressure Poisson equation in which the coefficient matrix is positive definite and symmetric. The advection and horizontal viscosity terms are discretized by use of a semi-Lagrangian approach. The resulting model is computationally efficient and unrestricted to the CFL condition. The developed model is verified against analytical solutions and experimental data, with excellent agreement.