Anisotropic mesh adaptation for the solution of the Stefan problem

Belhamadia, Youssef; Fortin, A.; Chamberland, Éric

doi:10.1016/j.jcp.2003.09.008

Cited by 61 publications

(54 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The anisotropic adaptive strategy used in this work was introduced in Fortin, Belhamadia and Chamberland [10,11] for phase change problems in cryotherapy. It was also used in [12,13] for drop deformation in two and three dimensions.…”

Section: Anisotropic Mesh Adaptationmentioning

confidence: 99%

See 1 more Smart Citation

An adaptive remeshing strategy for viscoelastic fluid flow simulations

Guénette

Fortin

Kane

et al. 2008

Journal of Non-Newtonian Fluid Mechanics

View full text Add to dashboard Cite

Section: Anisotropic Mesh Adaptationmentioning

confidence: 99%

“…The reader is referred once again to [10] for a complete description. As shall be seen, these local operations are sufficient to produce anisotropic meshes when needed.…”

Section: Anisotropic Mesh Adaptationmentioning

confidence: 99%

An adaptive remeshing strategy for viscoelastic fluid flow simulations

Guénette

Fortin

Kane

et al. 2008

Journal of Non-Newtonian Fluid Mechanics

View full text Add to dashboard Cite

“…To improve the accuracy on the interface location, a mesh adaptation method is used (see [19,20]). This method is based on a hierarchical error estimator.…”

Section: Interface Capturingmentioning

confidence: 99%

“…First, note the absence of shear stress in (20). Second, since the pressure is constant in the liquid matrix, the liquid-gas interface is a discontinuity surface (or line in 2D) for the pressure but the normal stress is continuous across this surface when surface tension is neglected.…”

Section: Analytical Modelmentioning

confidence: 99%

Direct 2D simulation of small gas bubble clusters: from the expansion step to the equilibrium state

Bruchon

Fortin

Bousmina

et al. 2006

Numerical Methods in Fluids

View full text Add to dashboard Cite

International audienceA numerical strategy, based on an adaptive finite element method, is proposed for the direct two-dimensional simulation of the expansion of small clusters of gas bubbles within a Newtonian liquid matrix. The velocity and pressure fields in the liquid are first defined through the Stokes equations and are subsequently extended to the gas bubbles. The liquid-gas coupling is imposed through the stress exerted on the liquid by gas pressure (ruled by an ideal gas law) and by surface tension. A level set method, combined with a mesh adaptation technique, is used to track liquid-gas interfaces. Many numerical simulations are presented. The single bubble case allows to compare the simulations to an analytical model. Simulations of the expansion of small clusters are then presented showing the interaction and evolution of the gas bubbles to an equilibrium state, involving topological rearrangements induced by Plateau's rule

show abstract

“…To improve the evaluation of the ow derivatives at the boundary, we propose to use high order Taylor series expansions around each boundary vertex. The method to extract ow derivatives using a least-squares method was demonstrated by Fortin et al [14]. We innovate by enforcing constraints on the least-squares method to ensure that the Taylor series are consistent with the boundary conditions.…”

Section: Boundary Conditions For Csementioning

confidence: 99%

On accurate boundary conditions for a shape sensitivity equation method

Duvigneau

Pelletier

2005

Numerical Methods in Fluids

View full text Add to dashboard Cite

SUMMARYThis paper studies the application of the continuous sensitivity equation method (CSEM) for the NavierStokes equations in the particular case of shape parameters. Boundary conditions for shape parameters involve ow derivatives at the boundary. Thus, accurate ow gradients are critical to the success of the CSEM. A new approach is presented to extract accurate ow derivatives at the boundary. High order Taylor series expansions are used on layered patches in conjunction with a constrained least-squares procedure to evaluate accurate ÿrst and second derivatives of the ow variables at the boundary, required for Dirichlet and Neumann sensitivity boundary conditions. The ow and sensitivity ÿelds are solved using an adaptive ÿnite-element method. The proposed methodology is ÿrst veriÿed on a problem with a closed form solution obtained by the Method of Manufactured Solutions. The ability of the proposed method to provide accurate sensitivity ÿelds for realistic problems is then demonstrated. The ow and sensitivity ÿelds for a NACA 0012 airfoil are used for fast evaluation of the nearby ow over an airfoil of di erent thickness (NACA 0015).

show abstract

Anisotropic mesh adaptation for the solution of the Stefan problem

Cited by 61 publications

References 13 publications

An adaptive remeshing strategy for viscoelastic fluid flow simulations

An adaptive remeshing strategy for viscoelastic fluid flow simulations

Direct 2D simulation of small gas bubble clusters: from the expansion step to the equilibrium state

On accurate boundary conditions for a shape sensitivity equation method

Contact Info

Product

Resources

About