Sharp interface Cartesian grid method III: Solidification of pure materials and binary solutions

Yang, Yi; Udaykumar, H. S.

doi:10.1016/j.jcp.2005.04.024

Cited by 57 publications

(48 citation statements)

References 62 publications

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“…In that work, the diffusion equation was solved using a boundary integral approach. Other authors have proposed successful approaches to both the Stefan problem and its extension to the solidification of binary alloys [160,162,151,167,142,164,141,7,52]. In the case of the Stefan problem, the two main ingredients are:…”

Section: A Level-set Approach To the Stefan Problemmentioning

confidence: 99%

High Resolution Sharp Computational Methods for Elliptic and Parabolic Problems in Complex Geometries

2012

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We present a review of some of the state-of-the-art numerical methods for solving the Stefan problem and the Poisson and the diffusion equations on irregular domains using (i) the level-set method for representing the (possibly moving) irregular domain's boundary, (ii) the ghost-fluid method for imposing the Dirichlet boundary condition at the irregular domain's boundary and (iii) a quadtree/octree nodebased adaptive mesh refinement for capturing small length scales while significantly reducing the memory and CPU footprint. In addition, we highlight common misconceptions and describe how to properly implement these methods. Numerical experiments illustrate quantitative and qualitative results.

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Section: A Level-set Approach To the Stefan Problemmentioning

confidence: 99%

High Resolution Sharp Computational Methods for Elliptic and Parabolic Problems in Complex Geometries

2012

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“…Computational methods for solving equations of flow around moving boundaries in the manner chosen here have been thoroughly validated in several papers [6][7][8][9] . Following fluid mechanical conventions, the governing equations are "non-dimensionalized" or normalized, by dividing dimensional quantities based on their corresponding representative scales in order to reveal parametric relationships to govern the physical behavior.…”

Section: Computational Modeling Of Transport and Mixing In Antroduodementioning

confidence: 99%

Mechanics of flow and mixing at antroduodenal junction

Dillard

Krishnan²,

Udaykumar

2007

WJG

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The morphology of tissue structures composing the pyloric orifice is thought to play a role in effectively mixing aqueous gastric effluent with duodenal secretions. To understand the physical mechanisms leading to efficient digestion requires computational models that allow for analyses of the contributions of individual structural components. Thus, we have simulated 2-D channel flows through representative models of the duodenum with moving boundary capabilities in order to quantitatively assess the importance of notable features. A well-tested flow solver was used to computationally i s o l a t e a n d c o m p a r e g e o m e t r i c a n d k i n e m a t i c parameters that lead to various characteristics of fluid motion at the antroduodenal junction. Scalar variance measurement was incorporated to quantify the mixing effectiveness of each component. It was found that the asymmetric geometry of the pyloric orifice in concert with intermittent gastric outflow and luminal constriction is likely to enhance homogenization of gastric effluent with duodenal secretions.

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“…One is to solve sharp-interface problems in which one or more variables (or their derivatives) are typically discontinuous across an interface, see, e.g. [1][2][3]. The other is to solve a system of parabolic equations in which the interface is specified by a level set of one of the variables, see, e.g.…”

Section: Introductionmentioning

confidence: 99%

An alternating Crank–Nicolson method for the numerical solution of the phase‐field equations using adaptive moving meshes

Tan

Huang

2007

Numerical Methods in Fluids

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SUMMARYAn alternating Crank-Nicolson method is proposed for the numerical solution of the phase-field equations on a dynamically adaptive grid, which automatically leads to two decoupled algebraic subsystems, one is linear and the other is semilinear. The moving mesh strategy is based on the approach proposed by Li et al. (J. Comput. Phys. 2001; 170:562-588) to separate the mesh-moving and partial differential equation evolution. The phase-field equations are discretized by a finite volume method in space, and the mesh-moving part is realized by solving the conventional Euler-Lagrange equations with the standard gradient-based monitors. The algorithm is computationally efficient and has been successfully used in numerical simulations.

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Sharp interface Cartesian grid method III: Solidification of pure materials and binary solutions

Cited by 57 publications

References 62 publications

High Resolution Sharp Computational Methods for Elliptic and Parabolic Problems in Complex Geometries

High Resolution Sharp Computational Methods for Elliptic and Parabolic Problems in Complex Geometries

Mechanics of flow and mixing at antroduodenal junction

An alternating Crank–Nicolson method for the numerical solution of the phase‐field equations using adaptive moving meshes

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