Finite-Element Methods for Free-Surface Flow

1994 ◽  
pp. 115-146
Author(s):  
John I. Finnie
Keyword(s):  
Finite Element ◽  
Free Surface ◽  
Finite Element Methods ◽  
Free Surface Flow ◽  
Surface Flow

scholarly journals The Finite Element Numerical Investigation of Free Surface Newtonian and Non-Newtonian Fluid Flows in the Rectangular Tanks

2020 ◽  
Vol 2020 ◽  
pp. 1-18
Author(s):  
Puyang Gao
Keyword(s):  
Finite Element ◽  
Free Surface ◽  
Level Set ◽  
Newtonian Fluid ◽  
Mass Conservation ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Two Phase ◽  
Navier Stokes Equation ◽  
Correction Technique

In this paper, we develop a new computational framework to investigate the sloshing free surface flow of Newtonian and non-Newtonian fluids in the rectangular tanks. We simulate the flow via a two-phase model and employ the fixed unstructured mesh in the computation to avoid the mesh distortion and reconstruction. As for the solution of Navier–Stokes equation, we utilize the SUPG finite element method based on the splitting scheme. The same order interpolation functions are then used for velocity and pressure. Moreover, the moving interface is captured via the concise level set method. We take advantage of the implicit discontinuous Galerkin method to handle the solution of level set and its reinitialization equations. A mass correction technique is also added to ensure the mass conservation property. The dam break-free surface flow is simulated firstly to demonstrate the validity of our mathematical model. In addition, the sloshing Newtonian fluid in the tank with flat and rough bottoms is considered to illustrate the feasibility and robustness of our computational scheme. Finally, the development of free surface for non-Newtonian fluid is also studied in the two tanks, and the influence of power-law index on the sloshing fluid flow is analyzed.

A dissipative finite element model for free surface flow

1988 ◽  
Vol 104 (1-4) ◽  
pp. 289-299 ◽  
Author(s):  
Litsa Anastasiadou-Partheniou ◽  
George A. Terzidis
Keyword(s):  
Finite Element ◽  
Free Surface ◽  
Finite Element Model ◽  
Free Surface Flow ◽  
Element Model ◽  
Surface Flow

A Finite Element Method for a Nonlinear Sloshing Problem

2003 ◽  
Author(s):  
J. H. Kyoung ◽  
J. W. Kim ◽  
K. J. Bai
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Free Surface ◽  
Impact Load ◽  
Surface Condition ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Time Step ◽  
Nonlinear Sloshing ◽  
Element Method

A nonlinear sloshing problem in LNG tanker is numerically simulated. During excessive sloshing, the sloshing-induced impact load can cause a critical damage on the tank structure. Recently, this problem became one of important issues in FPSO design. A three-dimensional free surface flow in a tank is formulated in the scope of potential flow theory. The exact nonlinear free surface condition is satisfied numerically. A finite-element method based on Hamilton’s principle is employed as a numerical scheme. The problem is treated as an initial-value problem. The computations are made through an iterative method at each time step. The hydrodynamic loading on the pillar in the tank is computed and compared with other results.

A Fractional Two-Step Finite Element Formulation for Unsteady Free Surface Flow Using ALE Method

2004 ◽  
Vol 261-263 ◽  
pp. 573-578
Author(s):  
Q. Li ◽  
H.Z. Liu ◽  
Zhuo Zhuang ◽  
S. Yamaguchi ◽  
Masao Toyoda
Keyword(s):  
Finite Element ◽  
Free Surface ◽  
Free Surface Flow ◽  
Linear Interpolation ◽  
Surface Flow ◽  
Finite Element Formulation ◽  
Element Formulation ◽  
Step Method ◽  
Fractional Step Method ◽  
Ale Method

A numerical algorithm using equal-order linear finite element and fractional two-step method is presented in this paper, which is used for analysis of incompressible viscous fluid flow with free surface problems. In order to avoid severe mesh distortions, ALE method is used for dealing with the free surface sloshing. For numerical integration, the fractional step method is employed, which is useful because the same linear interpolation functions for both velocity and pressure could be carried out in the finite element formulation. The present algorithm has been applied to some examples and proved to be accurate and more efficient.

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