Nonlocal transport equations in multiscale media. Modeling, dememorization, and discretizations
In this paper, we consider a class of convection-diffusion equations with memory effects. These equations arise as a result of homogenization or upscaling of linear transport equations in heterogeneous media and play an important role in many applications. First, we present a dememorization techniqu...
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ir-20.500.12258-234632025-02-11T13:00:24Z Nonlocal transport equations in multiscale media. Modeling, dememorization, and discretizations Vabishchevich, P. N. Вабищевич, П. Н. Nonlocal transport equations Multiscale media Discretizations Dememorization In this paper, we consider a class of convection-diffusion equations with memory effects. These equations arise as a result of homogenization or upscaling of linear transport equations in heterogeneous media and play an important role in many applications. First, we present a dememorization technique for these equations. We show that the convection-diffusion equations with memory effects can be written as a system of standard convection diffusion reaction equations. This allows removing the memory term and simplifying the computations. We consider a relation between dememorized equations and micro-scale equations, which do not contain memory terms. We note that dememorized equations differ from micro-scale equations and constitute a macroscopic model. Next, we consider both implicit and partially explicit methods. The latter is introduced for problems in multiscale media with high-contrast properties. Because of high-contrast, explicit methods are restrictive and require time steps that are very small (scales as the inverse of the contrast). We show that, by appropriately decomposing the space, we can treat only a few degrees of freedom implicitly and the remaining degrees of freedom explicitly. We present a stability analysis. Numerical results are presented that confirm our theoretical findings about partially explicit schemes applied to dememorized systems of equations. 2023-05-11T12:32:52Z 2023-05-11T12:32:52Z 2023 Статья Efendiev, Y., Leung, W.T., Li, W., Pun, S.-M., Vabishchevich, P.N. Nonlocal transport equations in multiscale media. Modeling, dememorization, and discretizations // Journal of Computational Physics. - 2023. - 472, № 111555. - DOI: 10.1016/j.jcp.2022.111555 http://hdl.handle.net/20.500.12258/23463 en Journal of Computational Physics application/pdf application/pdf |
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Репозиторий |
| language |
English |
| topic |
Nonlocal transport equations Multiscale media Discretizations Dememorization |
| spellingShingle |
Nonlocal transport equations Multiscale media Discretizations Dememorization Vabishchevich, P. N. Вабищевич, П. Н. Nonlocal transport equations in multiscale media. Modeling, dememorization, and discretizations |
| description |
In this paper, we consider a class of convection-diffusion equations with memory effects. These equations arise as a result of homogenization or upscaling of linear transport equations in heterogeneous media and play an important role in many applications. First, we present a dememorization technique for these equations. We show that the convection-diffusion equations with memory effects can be written as a system of standard convection diffusion reaction equations. This allows removing the memory term and simplifying the computations. We consider a relation between dememorized equations and micro-scale equations, which do not contain memory terms. We note that dememorized equations differ from micro-scale equations and constitute a macroscopic model. Next, we consider both implicit and partially explicit methods. The latter is introduced for problems in multiscale media with high-contrast properties. Because of high-contrast, explicit methods are restrictive and require time steps that are very small (scales as the inverse of the contrast). We show that, by appropriately decomposing the space, we can treat only a few degrees of freedom implicitly and the remaining degrees of freedom explicitly. We present a stability analysis. Numerical results are presented that confirm our theoretical findings about partially explicit schemes applied to dememorized systems of equations. |
| format |
Статья |
| author |
Vabishchevich, P. N. Вабищевич, П. Н. |
| author_facet |
Vabishchevich, P. N. Вабищевич, П. Н. |
| author_sort |
Vabishchevich, P. N. |
| title |
Nonlocal transport equations in multiscale media. Modeling, dememorization, and discretizations |
| title_short |
Nonlocal transport equations in multiscale media. Modeling, dememorization, and discretizations |
| title_full |
Nonlocal transport equations in multiscale media. Modeling, dememorization, and discretizations |
| title_fullStr |
Nonlocal transport equations in multiscale media. Modeling, dememorization, and discretizations |
| title_full_unstemmed |
Nonlocal transport equations in multiscale media. Modeling, dememorization, and discretizations |
| title_sort |
nonlocal transport equations in multiscale media. modeling, dememorization, and discretizations |
| publishDate |
2023 |
| url |
https://dspace.ncfu.ru/handle/20.500.12258/23463 |
| work_keys_str_mv |
AT vabishchevichpn nonlocaltransportequationsinmultiscalemediamodelingdememorizationanddiscretizations AT vabiŝevičpn nonlocaltransportequationsinmultiscalemediamodelingdememorizationanddiscretizations |
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