High-order time integrators for front-tracking finite-element analysis of viscous free-surface flows

2015 ◽  
Vol 77 (11) ◽  
pp. 668-693 ◽  
Author(s):  
L. Charlot ◽  
S. Etienne ◽  
A. Hay ◽  
D. Pelletier ◽  
A. Garon
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Free Surface ◽  
Front Tracking ◽  
Free Surface Flows ◽  
High Order ◽  
Element Analysis ◽  
Surface Flows ◽  
Time Integrators ◽  
High Order Time

scholarly journals Variational analysis for simulating free-surface flows in a porous medium

2003 ◽  
Vol 2003 (8) ◽  
pp. 377-396
Author(s):  
Shabbir Ahmed ◽  
Charles Collins
Keyword(s):  
Finite Element ◽  
Porous Medium ◽  
Free Surface ◽  
Free Surface Flows ◽  
Parabolic Partial Differential Equation ◽  
Element Analysis ◽  
Surface Flows ◽  
The Matrix ◽  
The Stability ◽  
Positive Definite System

A variational formulation has been developed to solve a parabolic partial differential equation describing free-surface flows in a porous medium. The variational finite element method is used to obtain a discrete form of equations for a two-dimensional domain. The matrix characteristics and the stability criteria have been investigated to develop a stable numerical algorithm for solving the governing equation. A computer programme has been written to solve a symmetric positive definite system obtained from the variational finite element analysis. The system of equations is solved using the conjugate gradient method. The solution generates time-varying hydraulic heads in the subsurface. The interfacing free surface between the unsaturated and saturated zones in the variably saturated domain is located, based on the computed hydraulic heads. Example problems are investigated. The finite element solutions are compared with the exact solutions for the example problems. The numerical characteristics of the finite element solution method are also investigated using the example problems.

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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