Stabilized edge-based finite element simulation of free-surface flows

2007 ◽  
Vol 54 (6-8) ◽  
pp. 965-993 ◽  
Author(s):  
Renato N. Elias ◽  
Alvaro L. G. A. Coutinho
Keyword(s):  
Finite Element ◽  
Free Surface ◽  
Finite Element Simulation ◽  
Free Surface Flows ◽  
Surface Flows ◽  
Element Simulation ◽  
Edge Based

Computational Techniques for Stabilized Edge-Based Finite Element Simulation of Nonlinear Free-Surface Flows

2009 ◽  
Vol 131 (4) ◽  
Author(s):  
Renato N. Elias ◽  
Milton A. Gonçalves ◽  
Alvaro L. G. A. Coutinho ◽  
Paulo T. T. Esperança ◽  
Marcos A. D. Martins ◽  
...  
Keyword(s):  
Finite Element ◽  
Free Surface ◽  
Finite Element Simulation ◽  
Free Surface Flows ◽  
Computational Techniques ◽  
Normal Velocity ◽  
Parallel Edge ◽  
Surface Flows ◽  
Element Simulation ◽  
Edge Based

Free-surface flows occur in several problems in hydrodynamics, such as fuel or water sloshing in tanks, waves breaking in ships, offshore platforms, harbors, and coastal areas. The computation of such highly nonlinear flows is challenging, since free-surfaces commonly present merging, fragmentation, and breaking parts, leading to the use of interface-capturing Eulerian approaches. In such methods the surface between two fluids is captured by the use of a marking function, which is transported in a flow field. In this work we discuss computational techniques for efficient implementation of 3D incompressible streamline-upwind/Petrov–Galerkin (SUPG)/pressure-stabilizing/Petrov–Galerkin finite element methods to cope with free-surface problems with the volume-of-fluid method (Elias, and Coutinho, 2007, “Stabilized Edge-Based Finite Element Simulation of Free-Surface Flows,” Int. J. Numer. Methods Fluids, 54, pp. 965–993). The pure advection equation for the scalar marking function was solved by a fully implicit parallel edge-based SUPG finite element formulation. Global mass conservation is enforced, adding or removing mass proportionally to the absolute value of the normal velocity of the interface. We introduce parallel edge-based data structures, a parallel dynamic deactivation algorithm to solve the marking function equation only in a small region around the interface. The implementation is targeted to distributed memory systems with cache-based processors. The performance and accuracy of the proposed solution method is tested in the simulation of the water impact on a square cylinder and in the propagation of a solitary wave.

Computational Techniques for Stabilized Edge-Based Finite Element Simulation of Free-Surface Flows

2008 ◽  
Author(s):  
Renato N. Elias ◽  
Milton A. Gonc¸alves ◽  
Alvaro L. G. A. Coutinho ◽  
Paulo T. T. Esperanc¸a ◽  
Marcos A. D. Martins ◽  
...  
Keyword(s):  
Finite Element ◽  
Free Surface ◽  
Free Surface Flows ◽  
Computational Techniques ◽  
Element Formulation ◽  
Normal Velocity ◽  
Parallel Edge ◽  
Surface Flows ◽  
Highly Nonlinear ◽  
Edge Based

Free-surface flows occur in several problems in hydrodynamics, such as fuel or water sloshing in tanks, waves breaking in ships, offshore platforms, harbors and coastal areas. The computation of such highly nonlinear flows is challenging since free-surfaces commonly present merging, fragmentation and breaking parts, leading to the use of interface capturing Eulerian approaches. In such methods the surface between two fluids is captured by the use of a marking function which is transported in a flow field. In this work we discuss computational techniques for efficient implementation of 3D incompressible SUPG/PSPG finite element methods to cope with free-surface problems with the Volume-of-Fluid (VOF) method [1]. The pure advection equation for the scalar marking function was solved by a fully implicit parallel edge-based SUPG finite element formulation. Global mass conservation is enforced adding or removing mass proportionally to the absolute value of the normal velocity of the interface. We introduce parallel edge-based data structures, a parallel dynamic deactivation algorithm to solve the marking function equation only in a small region around the interface. The implementation is targeted to distributed memory systems with cache-based processors. The performance and accuracy of the proposed solution method is tested in the simulation of the water impact on a square cylinder and in the propagation of a solitary wave.

scholarly journals Modeling Free Surface Flows Using Stabilized Finite Element Method

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Deepak Garg ◽  
Antonella Longo ◽  
Paolo Papale
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Free Surface ◽  
Numerical Scheme ◽  
Stokes Equations ◽  
Fluid Velocity ◽  
Computer Code ◽  
Free Surface Flows ◽  
Surface Flows ◽  
Element Method

This work aims to develop a numerical wave tank for viscous and inviscid flows. The Navier-Stokes equations are solved by time-discontinuous stabilized space-time finite element method. The numerical scheme tracks the free surface location using fluid velocity. A segregated algorithm is proposed to iteratively couple the fluid flow and mesh deformation problems. The numerical scheme and the developed computer code are validated over three free surface problems: solitary wave propagation, the collision between two counter moving waves, and wave damping in a viscous fluid. The benchmark tests demonstrate that the numerical approach is effective and an attractive tool for simulating viscous and inviscid free surface flows.

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