Numerical investigation of advection–diffusion in an inhomogeneous medium with a thin channel using the multiscale finite element method
| dc.citation.epage | 157 | |
| dc.citation.issue | 1 | |
| dc.citation.spage | 146 | |
| dc.contributor.affiliation | Львiвський нацiональний унiверситет iменi Iвана Франка | |
| dc.contributor.affiliation | Ivan Franko National University of Lviv | |
| dc.contributor.author | Мазуряк, Н. В. | |
| dc.contributor.author | Савула, Я. Г. | |
| dc.contributor.author | Mazuriak, N. V. | |
| dc.contributor.author | Savula, Ya. H. | |
| dc.date.accessioned | 2023-03-06T12:28:16Z | |
| dc.date.available | 2023-03-06T12:28:16Z | |
| dc.date.created | 2020-01-01 | |
| dc.date.issued | 2020-01-01 | |
| dc.description.abstract | Розглянуто задачу адвекцiї–дифузiї в неоднорiдному середовищi з тонким каналом. До розв’язування цiєї задачi застовано рiзномасштабний метод скiнченних елементiв. Показано, що отриманий розв’язок є стiйким та збiжним для достатньо великих чисел Пекле. Наведено та проаналiзовано результати обчислювальних експериментiв. | |
| dc.description.abstract | The advection-diffusion in an inhomogeneous medium with a thin channel is considered. The multiscale finite element method is applied to solving the formulated model problem. It is shown that the obtained solution is stable and convergent for sufficiently large Peclet numbers. Numerical examples are presented and analysed. | |
| dc.format.extent | 146-157 | |
| dc.format.pages | 12 | |
| dc.identifier.citation | Mazuriak N. V. Numerical investigation of advection–diffusion in an inhomogeneous medium with a thin channel using the multiscale finite element method / Mazuriak N. V., Savula Ya. H. // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2020. — Vol 7. — No 1. — P. 146–157. | |
| dc.identifier.citationen | Mazuriak N. V., Savula Ya. H. (2020) Numerical investigation of advection–diffusion in an inhomogeneous medium with a thin channel using the multiscale finite element method. Mathematical Modeling and Computing (Lviv), vol. 7, no 1, pp. 146-157. | |
| dc.identifier.doi | DOI: 10.23939/mmc2020.01.146 | |
| dc.identifier.uri | https://ena.lpnu.ua/handle/ntb/57509 | |
| dc.language.iso | en | |
| dc.publisher | Видавництво Львівської політехніки | |
| dc.publisher | Lviv Politechnic Publishing House | |
| dc.relation.ispartof | Mathematical Modeling and Computing, 1 (7), 2020 | |
| dc.relation.references | [1] Savula Ya. Numerical analysis of problems of mathematical physics by variational methods. Lviv, LNU(2004), (in Ukrainian). | |
| dc.relation.references | [2] Efendiev Y., Hou T. Multiscale finite element methods. Theory and application. New York, Springer– Verlag (2009). | |
| dc.relation.references | [3] Hou T., Wu X., Cai Z. Convergence of a multiscale finite element method for elliptic problems with rapidly oscillating coefficients. Mathematics of Computation. 68 (227), 913–943 (1999). | |
| dc.relation.references | [4] Spodar N., Savula Ya. Application of multiscale finite element method for solving the one-dimensional advection-diffusion problem. Physico-mathematical modelling and informational technologies. 19, 190–197 (2014), (in Ukrainian). | |
| dc.relation.references | [5] Spodar N., Savula Ya. Application of multiscale finite element method for solving the advection-diffusion problems. Visnyk of the Lviv University. Series Applied mathematics and informatics. 24, 92–100 (2016),(in Ukrainian). | |
| dc.relation.references | [6] Spodar N., Savula Ya. Computational aspects of multiscale finite element method. Physico-mathematical modelling and informational technologies. 23, 169–177 (2016), (in Ukrainian). | |
| dc.relation.references | [7] Mazuriak N., Savula Ya. Numerical analysis of the advection-diffusion problems in thin curvilinear channel based on multiscale finite element method. Mathematical modeling and computing. 4 (1), 59–68 (2017). | |
| dc.relation.references | [8] Savula Ya. H., Koukharskyi V. M., Chaplia Ye. Ya. Numerical analysis of advection-diffusion in the continuum with thin canal. Numerical Heat Transfer, Part A: Applications: An International Journal of Computation and Methodology. 33 (3), 341–351 (1998). | |
| dc.relation.references | [9] Kukharskyy V., Kukharska N., Savula Ya. Application of Heterogeneous Mathematical Models for the Solving of Heat and Mass Transfer Problems in Environments with Thin Heterogeneties. Physico-mathematical modelling and informational technologies. 4, 132–141 (2006), (in Ukrainian). | |
| dc.relation.references | [10] Rashevskij P. Course of differential geometry. Moscow, Leningrad, State publishing house of technical and theoretical literature (1950), (in Russian). | |
| dc.relation.referencesen | [1] Savula Ya. Numerical analysis of problems of mathematical physics by variational methods. Lviv, LNU(2004), (in Ukrainian). | |
| dc.relation.referencesen | [2] Efendiev Y., Hou T. Multiscale finite element methods. Theory and application. New York, Springer– Verlag (2009). | |
| dc.relation.referencesen | [3] Hou T., Wu X., Cai Z. Convergence of a multiscale finite element method for elliptic problems with rapidly oscillating coefficients. Mathematics of Computation. 68 (227), 913–943 (1999). | |
| dc.relation.referencesen | [4] Spodar N., Savula Ya. Application of multiscale finite element method for solving the one-dimensional advection-diffusion problem. Physico-mathematical modelling and informational technologies. 19, 190–197 (2014), (in Ukrainian). | |
| dc.relation.referencesen | [5] Spodar N., Savula Ya. Application of multiscale finite element method for solving the advection-diffusion problems. Visnyk of the Lviv University. Series Applied mathematics and informatics. 24, 92–100 (2016),(in Ukrainian). | |
| dc.relation.referencesen | [6] Spodar N., Savula Ya. Computational aspects of multiscale finite element method. Physico-mathematical modelling and informational technologies. 23, 169–177 (2016), (in Ukrainian). | |
| dc.relation.referencesen | [7] Mazuriak N., Savula Ya. Numerical analysis of the advection-diffusion problems in thin curvilinear channel based on multiscale finite element method. Mathematical modeling and computing. 4 (1), 59–68 (2017). | |
| dc.relation.referencesen | [8] Savula Ya. H., Koukharskyi V. M., Chaplia Ye. Ya. Numerical analysis of advection-diffusion in the continuum with thin canal. Numerical Heat Transfer, Part A: Applications: An International Journal of Computation and Methodology. 33 (3), 341–351 (1998). | |
| dc.relation.referencesen | [9] Kukharskyy V., Kukharska N., Savula Ya. Application of Heterogeneous Mathematical Models for the Solving of Heat and Mass Transfer Problems in Environments with Thin Heterogeneties. Physico-mathematical modelling and informational technologies. 4, 132–141 (2006), (in Ukrainian). | |
| dc.relation.referencesen | [10] Rashevskij P. Course of differential geometry. Moscow, Leningrad, State publishing house of technical and theoretical literature (1950), (in Russian). | |
| dc.rights.holder | ©2020 Lviv Polytechnic National University CMM IAPMM NASU | |
| dc.subject | рiзномасштабний метод скiнченних елементiв | |
| dc.subject | адвекцiя-дифузiя | |
| dc.subject | неоднорiдне середовище | |
| dc.subject | multiscale finite element method | |
| dc.subject | advection-diffusion | |
| dc.subject | inhomogeneous medium | |
| dc.subject.udc | 65N55 | |
| dc.subject.udc | 65N30 | |
| dc.subject.udc | 80M25 | |
| dc.subject.udc | 80A20 | |
| dc.title | Numerical investigation of advection–diffusion in an inhomogeneous medium with a thin channel using the multiscale finite element method | |
| dc.title.alternative | Числове дослідження адвекції–дифузії в неоднорідному середовищі з тонким каналом різномасштабним методом скінченних елементів | |
| dc.type | Article |