Simulation technique for wave generation. (English) Zbl 1069.76028

Aliabadi, S.; Abedi, J.; Zellars, B.; Bota, K.; Johnson, A.

Commun. Numer. Methods Eng. 19, No. 5, 349-359 (2003).

Summary: We present a finite element technique for simulation of water waves impacting on floating structures. The emphasis is on numerical methods for water wave generation and propagation. In our approach, the governing equations are Navier-Stokes equations written for two incompressible fluids. An interface function with two distinct values serves as a marker identifying the location of free surface. This function is transported throughout the computational domain with a time-dependent advection equation. The stabilized finite element formulations are written and integrated in an arbitrary Lagrangian-Eulerian domain. This allows us to handle the motion of physical boundaries, such as the wave generator surface, by moving the computational nodes. In the mesh-moving scheme, we assume that the computational domain is made of elastic materials. The linear elasticity equations are solved to obtain the displacements for each computational node. The numerical examples include 3D wave generation and wave breaking as they approach the coast, and the waves impacting on near-shore support columns.

MSC:

76M10	Finite element methods applied to problems in fluid mechanics
76D33	Waves for incompressible viscous fluids
76D27	Other free boundary flows; Hele-Shaw flows

Keywords:

free-surface flows; stabilized finite element formulation; Navier-Stokes equations

References:

[1]	Johnson A Aliabadi S Application of automatic mesh generation and mesh multiplication techniques to very large scale free-surface flow simulations 2000
[2]	Aliabadi, Free surface flow simulations using parallel finite element method, Simulation 75 (5) pp 256– (2000)
[3]	Aliabadi, Parallel simulation of flows in open channels, Journal of Future Generation Computer Systems 18 (5) pp 627– (2002) · Zbl 1042.68123
[4]	Aliabadi, Stabilized-finite-element/interface-capturing technique for parallel computation of un- steady flows with interfaces, Computer Methods in Applied Mechanics and Engineering 190 pp 243– (2000) · Zbl 0994.76050
[5]	Donea, An arbitrary Lagrangian-Eulerian finite element method for transient fluid-structure interactions, Computational Mechanics 33 pp 689– (1982) · Zbl 0508.73063
[6]	Farhat, Mixed explicit/implicit time integration of coupled aeroelastic problems: three-field formulation, geometric conservation and distributed solution, International Journal for Numerical Methods in Fluids 21 pp 807– (1995) · Zbl 0865.76038
[7]	Hirt, Volume of fluid (VOF) method for the dynamics of free boundaries, Journal of Computational Physics 39 pp 201– (1981) · Zbl 0462.76020
[8]	Sussman, A level set approach for computing incompressible two-phase flows, Journal of Computational Physics 114 pp 146– (1994) · Zbl 0808.76077
[9]	Johnson, Advanced mesh generation and update methods for 3D flow simulations, Computational Mechanics 23 pp 130– (1999) · Zbl 0949.76049
[10]	Aliabadi, Parallel fluid dynamics computations in aerospace applications, International Journal for Numerical Methods in Fluids 21 pp 783– (1995) · Zbl 0862.76033
[11]	Saad, GMRES: Generalized minimal residual algorithm for solving nonsymmetic linear systems, SIAM Journal of Scientific and Statistical Computing 7 pp 856– (1986)
[12]	Karypis, Parallel multilevel k-way partitioning scheme for irregular graphs, SIAM Review 41 (2) pp 278– (1999) · Zbl 0918.68073
[13]	Aliabadi, SUPG finite element computation of viscous compressible flows based on the conservation and entropy variables formulations, Computational Mechanics 11 pp 300– (1993) · Zbl 0772.76032