| 1. |
- Nepal, Surendra, et al.
(författare)
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A Moving Boundary approach of Capturing diffusants Penetration into Rubber : FEM Approximation and Comparison with laboratory Measurements
- 2021
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Ingår i: KGK Kautschuk, Gummi, Kunststoffe. - : Huethig GmbH & Co. KG. - 0948-3276. ; 74:5, s. 61-69
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Tidskriftsartikel (refereegranskat)abstract
- To model the penetration of diffusants into dense and foamed rubbers a moving -boundary scenario is proposed. After a brief discussion of scaling arguments, we present a finite element approximation of the moving boundary problem. To overcome numerical difficulties due to the a priori unknown motion of the diffusants penetration front, we transform the governing model equations from the physical domain with moving unknown boundary to a fixed fictitious domain. We then solve the transformed equations by the finite element method and explore the robustness of our approximations with respect to relevant model parameters. Finally, we discuss numerical estimations of the expected large -time behavior of the material.
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| 2. |
- Nepal, Surendra, 1990-
(författare)
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A moving boundary problem for capturing the penetration of diffusant concentration into rubbers : Modeling, simulation and analysis
- 2022
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- We propose a moving-boundary scenario to model the penetration of diffusants into rubbers. Immobilizing the moving boundary by using the well-known Landau transformation transforms the original governing equations into new equations posed in a fixed domain. We solve the transformed equations by the finite element method and investigate the parameter space by exploring the eventual effects of the choice of parameters on the overall diffusants penetration process. Numerical simulation results show that the computed penetration depths of the diffusant concentration are within the range of experimental measurements. We discuss numerical estimations of the expected large-time behavior of the penetration fronts. To have trust in the obtained simulation results, we perform the numerical analysis for our setting. Initially, we study semi-discrete finite element approximations of the corresponding weak solutions. We prove both a priori and a posteriori error estimates for the mass concentration of the diffusants, and respectively, for the a priori unknown position of the moving boundary. Finally, we present a fully discrete scheme for the numerical approximation of model equations. Our scheme is based on the Galerkin finite element method for the space discretization combined with the backward Euler method for time discretization. In addition to proving the existence and uniqueness of a solution to the fully discrete problem, we also derive a priori error estimates for the mass concentration of the diffusants, and respectively, for the position of the moving boundary that fit to our implementation in Python. Our numerical illustrations verify the obtained theoretical order of convergence in physical parameter regimes.
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| 3. |
- Nepal, Surendra, et al.
(författare)
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Analysis of a fully discrete approximation to a moving-boundary problem describing rubber exposed to diffusants
- 2023
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Ingår i: Applied Mathematics and Computation. - : Elsevier. - 0096-3003 .- 1873-5649. ; 442
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Tidskriftsartikel (refereegranskat)abstract
- We present a fully discrete scheme for the numerical approximation of a moving-boundary problem describing diffusants penetration into rubber. Our scheme utilizes the Galerkin finite element method for the space discretization combined with the backward Euler method for the time discretization. Besides dealing with the existence and uniqueness of solution to the fully discrete problem, we assume sufficient regularity for the solution to the target moving boundary problem and derive a a priori error estimates for the mass concentration of the diffusants, and respectively, for the position of the moving boundary. Our numerical results illustrate the obtained theoretical order of convergence in physical parameter regimes.
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| 4. |
- Nepal, Surendra, et al.
(författare)
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Error estimates for semi-discrete finite element approximations for a moving boundary problem capturing the penetration of diffusants into rubber
- 2022
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Ingår i: International Journal of Numerical Analysis & Modeling. - : ISCI-INST SCIENTIFIC COMPUTING & INFORMATION. - 1705-5105. ; 19:1, s. 101-125
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Tidskriftsartikel (refereegranskat)abstract
- We consider a moving boundary problem with kinetic condition that describes the diffusion of solvent into rubber and study semi-discrete finite element approximations of the corresponding weak solutions. We report on both a priori and a posteriori error estimates for the mass concentration of the diffusants, and respectively, for the a priori unknown position of the moving boundary. Our working techniques include integral and energy-based estimates for a nonlinear parabolic problem posed in a transformed fixed domain combined with a suitable use of the interpolation-trace inequality to handle the interface terms. Numerical illustrations of our FEM approximations are within the experimental range and show good agreement with our theoretical investigation. This work is a preliminary investigation necessary before extending the current moving boundary modeling to account explicitly for the mechanics of hyperelastic rods to capture a directional swelling of the underlying elastomer.
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| 5. |
- Nepal, Surendra
(författare)
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Models for capturing the penetration of a diffusant concentration into rubber : Numerical analysis and simulation
- 2024
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- 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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| 6. |
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| 7. |
- Nepal, Surendra, et al.
(författare)
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Random walks and moving boundaries : Estimating the penetration of diffusants into dense rubbers
- 2023
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Ingår i: Probabilistic Engineering Mechanics. - : Elsevier. - 0266-8920 .- 1878-4275. ; 74
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Tidskriftsartikel (refereegranskat)abstract
- For certain materials science scenarios arising in rubber technology, one-dimensional moving boundary problems with kinetic boundary conditions are capable of unveiling the large-time behavior of the diffusants penetration front, giving a direct estimate on the service life of the material. Driven by our interest in estimating how a finite number of diffusant molecules penetrate through a dense rubber, we propose a random walk algorithm to approximate numerically both the concentration profile and the location of the sharp penetration front. The proposed scheme decouples the target evolution system in two steps: (i) the ordinary differential equation corresponding to the evaluation of the speed of the moving boundary is solved via an explicit Euler method, and (ii) the associated diffusion problem is solved by a random walk method. To verify the correctness of our random walk algorithm we compare the resulting approximations to computational results based on a suitable finite element approach with a controlled convergence rate. Our numerical results recover well penetration depth measurements of a controlled experiment designed specifically for this setting.
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