Finite difference method for 2-D and 3-D nonlinear free surface wave problems

1985 ◽  
Vol 1 (2) ◽  
pp. 117-130 ◽  
Author(s):  
Lü Yulin ◽  
Li Baoyuan
Keyword(s):  
Free Surface ◽  
Surface Wave ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Free Surface Wave ◽  
Nonlinear Free Surface ◽  
Wave Problems

Effects of Viscosity and Free-Surface Nonlinearity on the Wave Motion Generated by an Oscillating Twin Hull

2012 ◽  
Author(s):  
Palaniswamy Ananthakrishnan
Keyword(s):  
Free Surface ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Potential Flow ◽  
Wave Motion ◽  
Stokes Equations ◽  
Curvilinear Coordinates ◽  
Linear Potential ◽  
Nonlinear Free Surface

The hydrodynamics of a rectangular, floating twin hull under heave oscillation is analyzed to determine viscous and nonlinear effects on the radiation hydrodynamics of multi-hulls, in particular, at the resonant frequency corresponding to the piston (Helmholtz) mode of wave motions. A second-order finite-difference method based on boundary-fitted coordinates is used for the solution of the incompressible Navier-Stokes equations together with exact nonlinear viscous boundary conditions. To separate the viscosity effects from the nonlinear free-surface effects, through comparison of results, nonlinear inviscid results are also obtained using a boundary-fitted curvilinear coordinates based finite difference method. The nonlinear inviscid algorithm is based on the Eulerian-Lagrangian formulation of the nonlinear free-surface flow. The nonlinear results are compared with the linear potential-flow results obtained by Yeung and Seah [20] to quantify the combined nonlinear and viscous effects on the wave forces. The present results show the overall behavior of the wave motion to be similar to that predicted by the linear potential-flow theory [20]. Our results show that the effects of nonlinearity and viscosity on the wave motion can be significant for the Helmholtz mode, particularly for small separation distance between the hulls, which result in large vertical oscillation of the mean surface between the hulls. For small amplitudes of oscillation, the hydrodynamic pressure forces computed in the present analysis are in striking agreement with that given by the linear potential-flow analysis of Yeung and Seah [20].

2-D poroelastic wave modelling with a topographic free surface by the curvilinear grid finite-difference method

2019 ◽  
Vol 218 (3) ◽  
pp. 1961-1982 ◽  
Author(s):  
Yao-Chong Sun ◽  
Hengxin Ren ◽  
Xu-Zhen Zheng ◽  
Na Li ◽  
Wei Zhang ◽  
...  
Keyword(s):  
Free Surface ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Wave Modelling ◽  
Curvilinear Grid

Application of a generalized finite difference method to mould filling process

2017 ◽  
Vol 29 (3) ◽  
pp. 450-469 ◽  
Author(s):  
E. O. RESÉNDIZ-FLORES ◽  
J. KUHNERT ◽  
F. R. SAUCEDO-ZENDEJO
Keyword(s):  
Free Surface ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Stokes Equations ◽  
Free Surface Flows ◽  
Three Dimensions ◽  
Navier Stokes ◽  
Filling Process ◽  
Mould Filling

This paper proposes the use of a generalized finite difference method for the numerical simulation of free surface single phase flows during mould filling process which are common in some industrial processes particularly in the area of metal casting. A novel and efficient idea for the computation of the normal vectors for free surface flows is introduced and presented for the first time. The incompressible Navier–Stokes equations are numerically solved by the well-known Chorin's projection method. After we showed the main ideas behind the meshless approach, some numerical results in two and three dimensions are presented corresponding to mould filling process simulation.

The Effect of Defects on Rock Fracturing under Dynamic Loads

2011 ◽  
Vol 230-232 ◽  
pp. 278-282 ◽  
Author(s):  
Zhe Ming Zhu
Keyword(s):  
Free Surface ◽  
Equation Of State ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Defect Density ◽  
Dynamic Loads ◽  
Test Results ◽  
Rock Fracturing ◽  
Simulation Results

A surface blasting model of rock with pre-existing randomly distributed defects, including voids, pores and small open joints, under blasting loads are established by using finite difference method. A shock equation of state, obtained from the existing test results, is employed for the granite near the explosive charge, and for the granite far from the charge, a linear EOS is applied. The granite dynamic strengths, which increase with strain rate, are calculated based on the existing test results. The simulation results show that under blasting, most of cracks are initiated at the defect tips independently; the damage range increases as defect density decreases;spalling is easily happening near a free surface as there is a blasting near the surface.

Sign in / Sign up

Export Citation Format

Share Document