The Implementation of the Level Set Method Within the Finite Element Formulation

2000 ◽  
Author(s):  
Sergey V. Shepel ◽  
Samuel Paolucci
Keyword(s):  
Finite Element ◽  
Level Set Method ◽  
Level Set ◽  
Mass Conservation ◽  
Significant Loss ◽  
Finite Element Formulation ◽  
Advection Equation ◽  
Element Formulation ◽  
Loss Of Mass ◽  
Finite Element Schemes

Abstract We apply the Streamline Upwind Petrov Galerkin (SUPG) finite element formulation of the Level Set method to 2D redistancing and advection problems on unstructured triangulated grids. The purpose is to test the Level Set method for mass conservation properties, where the mass is understood as the amount of fluid enclosed by the interface. For the redistancing procedure we implement the idea of mass correction suggested by Sussman and Fatemi (1999) and confirm its high accuracy within the finite element formulation. However, we find that the use of the first order SUPG formulation of the Level Set method for coupled redistancing-advection problems can result in significant loss of mass caused by distortion of the interface due to numerical diffusion. This neccesitates the use of higher order upwind finite element schemes for the advection equation.

On the Use of the Level Set Method With Unstructured Grids

2001 ◽  
Author(s):  
Sergey V. Shepel ◽  
Samuel Paolucci
Keyword(s):  
Finite Element ◽  
Level Set Method ◽  
Level Set ◽  
Unstructured Grids ◽  
Finite Element Formulation ◽  
Element Formulation ◽  
Level Set Function ◽  
Complicated Geometry ◽  
Rkdg Finite Element Method ◽  
Set Function

Abstract A mass preserving finite element formulation of the Level Set method is presented. The formulation is based on the discontinuous representation of the level set function and involves the Runge-Kutta Discontinuous Galerkin (RKDG) finite element method. The resulting formulation has the flexibility of treating a complicated geometry by using arbitrary triangulation. The performance of the scheme is demonstrated on a number of two-dimensional re-distance and coupled advection-redistance problems. The results indicate that the RKDG finite element formulation provides accurate solutions of the Level Set problem and has great potential in fluid dynamics applications.

scholarly journals A novel level-set finite element formulation for grain growth with heterogeneous grain boundary energies

2018 ◽  
Vol 160 ◽  
pp. 578-590 ◽  
Author(s):  
Julien Fausty ◽  
Nathalie Bozzolo ◽  
Daniel Pino Muñoz ◽  
Marc Bernacki
Keyword(s):  
Finite Element ◽  
Grain Boundary ◽  
Grain Growth ◽  
Level Set ◽  
Finite Element Formulation ◽  
Element Formulation

scholarly journals Improving the mass conservation of the level set method in a finite element context

2010 ◽  
Vol 348 (9-10) ◽  
pp. 535-540 ◽  
Author(s):  
Aymen Laadhari ◽  
Pierre Saramito ◽  
Chaouqi Misbah
Keyword(s):  
Finite Element ◽  
Level Set Method ◽  
Level Set ◽  
Mass Conservation

A Numerical Study on the Entry Problem of an Elastic Body Using Level Set Method and Combined Formulation

2011 ◽  
Author(s):  
Hyoung Gwon Choi
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Free Surface ◽  
Elastic Body ◽  
Level Set Method ◽  
Level Set ◽  
Mixed Finite Element ◽  
Element Formulation ◽  
Surface Tracking ◽  
Element Method

A finite element method based on level set and combined formulation was studied for the analysis of entry problem of an elastic body. Both free surface tracking and the interaction of an entry body with the fluid flow need to be considered in the entry problem. Free surface tracking was achieved using a level set method in which advection and reinitialization equations for level set variable were discretized using a least square finite element method. The coupling of the motion of the elastic body with fluid flow was conducted using combined mixed finite element formulation. ALE (arbitrary Lagrangian Eulerian) method was adopted for the movement of a grid since the downward motion of the body is dominant in entry problem. Since a mixed finite element is adopted, a linear basis function that belongs to H1 space is used for velocity and level set variables on each sub-element (Th) while a linearly interpolated pressure variable that belongs to L2 space is adopted on each element (T2h). The level set method based on a least square finite element method was verified by solving some free surface tracking problems and then, the finite element formulation for entry problem was validated by comparing with an existing experimental results. Further, the comparison of the entry of an elastic body with that of a rigid body was investigated.

Sign in / Sign up

Export Citation Format

Share Document