A numerical model for vertical two-dimensional non-hydrostatic free surface flows
Résumé
Abstract In this paper we describe the development of a two-dimensional vertical non-hydrostaticnumerical model for simulating free surface flows. The model is basedon the solution of the two-dimensional incompressible Navier-Stokes equations inthe sigma-coordinate system. The governing equations are discretized using the finite difference approximation on non-staggered grid and solved based on the algorithm of a projection method, which consists of combining the momentum and continuity equations to establish a Poisson-type equation for the pressure. To predict the moving free surface elevations, the depth-integrated continuity equation is used and solved explicitly by the total variation diminishing Lax-Wendroff scheme. To circumvent the limitations of overly restrictive time steps due to a high aspect ratio between horizontal and vertical spatial discretization. We adopt a strategy based on a split between the advection-diffusion part and the projection part. The advection-diffusion is also split so that it is treated implicitly in the vertical direction and explicitly in the horizontal direction. This discretization technique has enabled us to group the resulting finite difference equations with the appropriate boundary conditions in the form of linear tridiagonal systems with the intermediate velocities as unknowns, which can be efficiently inverted using the Thomas algorithm. The model has been applied to simulate five benchmark-tests of surface wave motions. Comparison between numerical results, analytical solutions and experimental data demonstrates asatisfactory performance. MSC Classification: 65M06, 65N06, 76D05, 76M20, 76D33
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