Numerical simulation of Stefan problem with ensuing melt flow through XFEM/level set method

Li, Min; Chaouki, Hicham; Robert, Jean-Loup; Ziegler, Donald; Martin, Dave; Fafard, Mario

doi:10.1016/j.finel.2018.05.008

Cited by 13 publications

(4 citation statements)

References 38 publications

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“…The final addition of the hydrodynamic calculation with buoyancy was applied in Martin et al [29,30], but the methodology made no enrichment in the approximation of the velocity and pressure fields. It was not until Li et al [31] that XFEM with LSM coupled the Stefan and hydrodynamic problems and considered non-constant density phase changes and buoyancy effects. However, to the author's knowledge, there is no full Navier-Stokes implementation of the coupled problem that is able to simulate phase change at high Reynolds numbers.…”

Section: Research Motivationmentioning

confidence: 99%

Fluid-structure interaction: Extended-FEM approach to solidification

Caraeni

Casseau

Habashi

2020

Finite Elements in Analysis and Design

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The ability of in-flight icing numerical codes to account for the effects of Supercooled Large Droplets (SLD), which are droplets ranging from 50-1000 µm, is still somewhat limited. Solvers that simulate SLD in in-flight icing treat an ensemble of droplets adopting a macroscopic approach, making use of some heuristic correlations based on experiments or extrapolating SLD behavior from smaller non-SLD droplets. Alternatively, taking a microscopic approach and accurately simulating the physics of individual droplets can lead to higher fidelity models when replacing empirical data. Therefore, developing models of a single SLD droplet impingement and solidification can provide a framework that expands the capabilities of current macroscopic solvers to handle water-ice fluid-structure interactions (FSI) and solidification.This presents challenges such as the evolution of the water-ice interface and the jump in fluid/solid properties due to phase change. This thesis proposes a level set method (LSM) to capture the movement of the interface, and the extended finite element method (XFEM) to sharply account for the discontinuities in the material properties without the need for body-conforming meshes.

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Section: Research Motivationmentioning

confidence: 99%

Fluid-structure interaction: Extended-FEM approach to solidification

Caraeni

Casseau

Habashi

2020

Finite Elements in Analysis and Design

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“…Due to the complex nature of the problem, where the location of phase interfaces varies with time, only a limited number of analytical solutions are available 55 . Numerical techniques are therefore widely used to model the discontinuous temperature gradient field at phase interfaces 56‐60 Two‐phase flows A flow consisting of different phases (see Figure 1C) is commonplace in industrial applications such as oil and gas in pipelines, and water and steam in nuclear reactor cooling systems 61 .…”

Section: Introductionmentioning

confidence: 99%

“…55 Numerical techniques are therefore widely used to model the discontinuous temperature gradient field at phase interfaces. [56][57][58][59][60] • Two-phase flows A flow consisting of different phases (see Figure 1C) is commonplace in industrial applications such as oil and gas in pipelines, and water and steam in nuclear reactor cooling systems. 61 Since these phases have different properties, the interface between them can result in discontinuous velocity/pressure fields (under a slip condition) and their corresponding gradient fields.…”

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confidence: 99%

An object‐oriented geometric engine design for discontinuities in unfitted/immersed/enriched finite element methods

Zhang

Zhebel

Boom

et al. 2022

Numerical Meth Engineering

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In this work, an object-oriented geometric engine is proposed to solve problems with discontinuities, for instance, material interfaces and cracks, by means of unfitted, immersed, or enriched finite element methods (FEMs). Both explicit and implicit representations, such as geometric entities and level sets, are introduced to describe configurations of discontinuities. The geometric engine is designed in an object-oriented way and consists of several modules. For efficiency, a k-d tree data structure that partitions the background mesh is constructed for detecting cut elements whose neighbors are found by means of a dual graph structure. Moreover, the implementation for creating enriched nodes, integration elements, and physical groups is described in detail, and the corresponding pseudo-code is also provided. The complexity and efficiency of the geometric engine are investigated by solving 2-D and 3-D discontinuous models. The capability of the geometric engine is demonstrated on several numerical examples. Topology optimization and problems with intersecting discontinuities are handled with enriched FEMs, where enriched discretizations obtained from the geometric engine are used for the analysis. Furthermore, polycrystalline structures that overlap with an unfitted mesh are considered, where integration elements are created so they align with grain boundaries.Another example shows that the Stanford bunny, which is discretized by a surface mesh with triangular elements, can be fully immersed into a 3-D background mesh. Finally, we share a list of main findings and conclude that the proposed geometric engine is general, robust, and efficient. K E Y W O R D Sdiscontinuities, enriched finite element methods, geometric engine, level set, mesh generator INTRODUCTIONCommercial softwares such as Abaqus, Ansys, and COMSOL, have become the industry standard for finite element (FE) numerical analysis. They require, however, FE meshes that fit the problems' geometries, that is, where the edges of finiteThis is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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“…The jump in pressure is not considered. Recently, Li et al [20] and Martin et al [21] consider the XFEM method to solve two-dimensional solidification problems including natural convection. They use abs-enrichment scheme for the temperature approximation, while the sign-enrichment scheme for the melt velocity and pressure.…”

Section: Introductionmentioning

confidence: 99%

Archive of Mechanical Engineering

Stąpór

2019

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This paper presents an extended finite element method applied to solve phase change problems taking into account natural convection in the liquid phase. It is assumed that the transition from one state to another, e.g., during the solidification of pure metals, is discontinuous and that the physical properties of the phases vary across the interface. According to the classical Stefan condition, the location, topology and rate of the interface changes are determined by the jump in the heat flux. The incompressible Navier-Stokes equations with the Boussinesq approximation of the natural convection flow are solved for the liquid phase. The no-slip condition for velocity and the melting/freezing condition for temperature are imposed on the interface using penalty method. The fractional four-step method is employed for analysing conjugate heat transfer and unsteady viscous flow. The phase interface is tracked by the level set method defined on the same finite element mesh. A new combination of extended basis functions is proposed to approximate the discontinuity in the derivative of the temperature, velocity and the pressure fields. The single-mesh approach is demonstrated using three two-dimensional benchmark problems. The results are compared with the numerical and experimental data obtained by other authors.

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Numerical simulation of Stefan problem with ensuing melt flow through XFEM/level set method

Cited by 13 publications

References 38 publications

Fluid-structure interaction: Extended-FEM approach to solidification

Fluid-structure interaction: Extended-FEM approach to solidification

An object‐oriented geometric engine design for discontinuities in unfitted/immersed/enriched finite element methods

Archive of Mechanical Engineering

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