The Stefan problem with moving boundary

Rincon, Mauro A.; Scardua, A

doi:10.5269/bspm.v26i1-2.7412

Cited by 2 publications

(1 citation statement)

References 8 publications

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“…The explicit Finite Deference Method was used in (Savovic and Caldwell, 2003). The Faedo-Galerkin Finite Element Method with a Crank-Nicolson time scheme was used in (Rincon and Scardua, 2008). The numerical simulation of ice formation in one and two dimension using the cell-centered Finite Volume Method based on the latent heat source approach was investigated in (Prapainop and Maneeratana, 2004).…”

Section: Introductionmentioning

confidence: 99%

Numerical Simulation of Ice Melting Using the Finite Volume Method

Abdulkareem

2023

jcoeng

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The Aim of this paper is to investigate numerically the simulation of ice melting in one and two dimension using the cell-centered finite volume method. The mathematical model is based on the heat conduction equation associated with a fixed grid, latent heat source approach. The fully implicit time scheme is selected to represent the time discretization. The ice conductivity is chosento be the value of the approximated conductivity at the interface between adjacent ice and water control volumes. The predicted temperature distribution, percentage melt fraction, interface location and its velocity is compared with those obtained from the exact analytical solution. A good agreement is obtained when comparing the numerical results of one dimensional temperaturedistribution with the analytical results.

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Section: Introductionmentioning

confidence: 99%

Numerical Simulation of Ice Melting Using the Finite Volume Method

Abdulkareem

2023

jcoeng

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Advances Towards a Comprehensive Model of Laser-Rock Interaction

Alerigi

Batarseh

Assiri

2020

Day 2 Tue, November 03, 2020

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Laser applications provide unique advantages to applications in discovery, recovery, and production of hydrocarbons. A comprehensive numerical model would enable prediction, optimization, increase efficiency, enhance control, and further innovation. This work reviews the modeling methods, discusses key variables and physics, presents results, and introduces innovative solutions that make use of machine learning and artificial intelligence to solve an inherently multi-scale and multi-physics problem. Two possible methods have been explored to model laser-rock interaction: mechanistic and statistical — the former uses as a set of coupled partial differential equations that adequately describe the physics involved. The statistical method uses advanced statistical analysis and supervised-learning to elucidate relations between the experimental settings and observations. The full-physics or mechanistic model was developed using finite-element and finite-difference methods; it incorporates coupled solvers for electromagnetic, thermodynamics, and geomechanics. The statistical model uses advanced statistical analysis and machine learning to characterize the dynamics and build a prediction algorithm. A numerical model of laser-rock interaction must comprise physical dynamics that span over different time and spatial scales. When a laser beam impinges on a rock, a portion of the incident energy is absorbed as thermal energy, and a thermal gradient is created. The result is a distribution of physical and chemical changes such as spallation, melting, dissociation, calcination, or vaporization. The full-physical model can adequately capture the transient process; however, it requires a functional characterization of the dynamic rock properties, environmental conditions, and laser parameters. The statistical approach provides a prediction of the overall outcome of the process departing as a function of known input parameters, yet its precision depends on the availability of experimental data (outcomes and conditions). Key parameters are identified using statistical analysis. The modeling results agreed with experimental tests. Further, they evince that thermal properties and geomechanical stresses configuration have a significant impact on the process’ outcome. These methods can optimize and predict the interaction for multiple applications, ranging from heat treatment to stimulation. Subsurface laser operations could provide the next generation of stimulation and workover tools for Oil and Gas. Numerical models of laser-rock interaction are essential to predict, optimize, adapt, and evaluate subsurface laser applications during development, test, and operation. This work provides a basis for the development of future numerical models and enables the next generation of subsurface photonic tools.

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The Stefan problem with moving boundary

Cited by 2 publications

References 8 publications

Numerical Simulation of Ice Melting Using the Finite Volume Method

Numerical Simulation of Ice Melting Using the Finite Volume Method

Advances Towards a Comprehensive Model of Laser-Rock Interaction

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