Online Multiscale Finite Element Simulation of Thermo-Mechanical Model with Phase Change
This paper presents a thermo-mechanical model with phase transition considering changes in the mechanical properties of the medium. The proposed thermo-mechanical model is described by a system of partial differential equations for temperature and displacements. In the model, soil deformations occur...
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MDPI AG
2023-03-01
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| Series: | Computation |
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| Online Access: | https://www.mdpi.com/2079-3197/11/4/71 |
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| author | Dmitry Ammosov Maria Vasilyeva |
| author_facet | Dmitry Ammosov Maria Vasilyeva |
| author_sort | Dmitry Ammosov |
| collection | DOAJ |
| description | This paper presents a thermo-mechanical model with phase transition considering changes in the mechanical properties of the medium. The proposed thermo-mechanical model is described by a system of partial differential equations for temperature and displacements. In the model, soil deformations occur due to porosity growth caused by ice and water density differences. A finite-element approximation of this model on a fine grid is presented. The linearization from the previous time step is used to handle the nonlinearity of the problem. For reducing the size of the discrete problem, offline and online multiscale approaches based on the Generalized Multiscale Finite Element Method (GMsFEM) are proposed. A two-dimensional model problem simulating the heaving process of heterogeneous soil with a stiff inclusion was considered for testing the mathematical model and the multiscale approaches. Numerical solutions depict the process of soil heaving caused by changes in porosity due to the phase transition. The movement of the phase transition interface was observed. The change of medium properties, including the elastic modulus, was traced and corresponds to the phase transition interface. The proposed multiscale approaches significantly reduce the size of the discrete problem while maintaining reasonable accuracy. However, the online multiscale approach achieves better accuracy than the offline approach with fewer degrees of freedom. |
| first_indexed | 2024-03-11T05:06:57Z |
| format | Article |
| id | doaj.art-63a4da4cc31948a5bc5595df9ef0bcc2 |
| institution | Directory Open Access Journal |
| issn | 2079-3197 |
| language | English |
| last_indexed | 2024-03-11T05:06:57Z |
| publishDate | 2023-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Computation |
| spelling | doaj.art-63a4da4cc31948a5bc5595df9ef0bcc22023-11-17T18:49:04ZengMDPI AGComputation2079-31972023-03-011147110.3390/computation11040071Online Multiscale Finite Element Simulation of Thermo-Mechanical Model with Phase ChangeDmitry Ammosov0Maria Vasilyeva1Laboratory of Computational Technologies for Modeling Multiphysical and Multiscale Permafrost Processes, North-Eastern Federal University, 677980 Yakutsk, RussiaDepartment of Mathematics and Statistics, Texas A&M University-Corpus Christi, Corpus Christi, TX 78412, USAThis paper presents a thermo-mechanical model with phase transition considering changes in the mechanical properties of the medium. The proposed thermo-mechanical model is described by a system of partial differential equations for temperature and displacements. In the model, soil deformations occur due to porosity growth caused by ice and water density differences. A finite-element approximation of this model on a fine grid is presented. The linearization from the previous time step is used to handle the nonlinearity of the problem. For reducing the size of the discrete problem, offline and online multiscale approaches based on the Generalized Multiscale Finite Element Method (GMsFEM) are proposed. A two-dimensional model problem simulating the heaving process of heterogeneous soil with a stiff inclusion was considered for testing the mathematical model and the multiscale approaches. Numerical solutions depict the process of soil heaving caused by changes in porosity due to the phase transition. The movement of the phase transition interface was observed. The change of medium properties, including the elastic modulus, was traced and corresponds to the phase transition interface. The proposed multiscale approaches significantly reduce the size of the discrete problem while maintaining reasonable accuracy. However, the online multiscale approach achieves better accuracy than the offline approach with fewer degrees of freedom.https://www.mdpi.com/2079-3197/11/4/71permafrostheterogeneous mediumthermo-mechanicsphase changeonline generalized multiscale finite element method |
| spellingShingle | Dmitry Ammosov Maria Vasilyeva Online Multiscale Finite Element Simulation of Thermo-Mechanical Model with Phase Change Computation permafrost heterogeneous medium thermo-mechanics phase change online generalized multiscale finite element method |
| title | Online Multiscale Finite Element Simulation of Thermo-Mechanical Model with Phase Change |
| title_full | Online Multiscale Finite Element Simulation of Thermo-Mechanical Model with Phase Change |
| title_fullStr | Online Multiscale Finite Element Simulation of Thermo-Mechanical Model with Phase Change |
| title_full_unstemmed | Online Multiscale Finite Element Simulation of Thermo-Mechanical Model with Phase Change |
| title_short | Online Multiscale Finite Element Simulation of Thermo-Mechanical Model with Phase Change |
| title_sort | online multiscale finite element simulation of thermo mechanical model with phase change |
| topic | permafrost heterogeneous medium thermo-mechanics phase change online generalized multiscale finite element method |
| url | https://www.mdpi.com/2079-3197/11/4/71 |
| work_keys_str_mv | AT dmitryammosov onlinemultiscalefiniteelementsimulationofthermomechanicalmodelwithphasechange AT mariavasilyeva onlinemultiscalefiniteelementsimulationofthermomechanicalmodelwithphasechange |