Coupled partition of unity-level set finite element formulation for CO2 geo-sequestration

2014 ◽  
pp. 365-394
Keyword(s):  
Finite Element ◽  
Level Set ◽  
Partition Of Unity ◽  
Finite Element Formulation ◽  
Element Formulation

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

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.

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