Stochastic Solutions of Stefan Problems with General Time-Dependent Boundary Conditions

Ögren, Magnus

doi:10.1007/978-3-031-17820-7_29

Cited by 1 publication

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“…This approach simulates the stochastic motion of a finite number of individual particles, known as walkers. When solving a moving-boundary problem using RWM, it is essential to ensure an accurate representation of boundary conditions, including the moving-boundary associated with phase change [39,7].…”

Section: Motivation Methodology and Research Questionsmentioning

confidence: 99%

Models for capturing the penetration of a diffusant concentration into rubber: Numerical analysis and simulation

Nepal

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Understanding the transport of diffusants into rubber plays an important role in forecasting the material's durability. In this regard, we study different models, conduct numerical analysis, and present simulation results that predict the evolution of the penetration front of diffusants. We start with a moving-boundary approach to model this phenomenon, employing a numerical scheme to approximate the diffusant profile and the position of the moving boundary capturing the penetration front. Our numerical scheme utilizes the Galerkin finite element method for space discretization and the backward Euler method for time discretization. We analyze both semi-discrete and fully discrete approximations of the weak solution to the model equations, proving error estimates and demonstrating good agreement between numerical and theoretical convergence rates. Numerically approximated penetration front of the diffusant recovers well the experimental data. As an alternative approach to finite element approximation, we introduce a random walk algorithm that employs a finite number of particles to approximate both the diffusant profile and the location of the penetration front. The transport of diffusants is due to unbiased randomness, while the evolution of the penetration front is based on biased randomness. Simulation results obtained via the random walk approach are comparable with the one based on the finite element method. In a multi-dimensional scenario, we consider a strongly coupled elliptic-parabolic two-scale system with nonlinear dispersion that describes particle transport in porous media. We construct two numerical schemes approximating the weak solution to the two-scale model equations. We present simulation results obtained with both schemes and compare them based on computational time and approximation errors in suitable norms. By introducing a precomputing strategy, the computational time for both schemes is significantly improved.

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Section: Motivation Methodology and Research Questionsmentioning

confidence: 99%

Models for capturing the penetration of a diffusant concentration into rubber: Numerical analysis and simulation

Nepal

View full text Add to dashboard Cite

show abstract

Stochastic Solutions of Stefan Problems with General Time-Dependent Boundary Conditions

Cited by 1 publication

References 12 publications

Models for capturing the penetration of a diffusant concentration into rubber: Numerical analysis and simulation

Models for capturing the penetration of a diffusant concentration into rubber: Numerical analysis and simulation

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