1. MMC
  2. All Volumes and Issues
  3. Volume 7, Number 1, 2020
  4. Numerical investigation of advection-diffusion in an inhomogeneous medium with a thin channel using the multiscale finite element method

Numerical investigation of advection-diffusion in an inhomogeneous medium with a thin channel using the multiscale finite element method

MMC.
2020;
Volume 7, Number 1
: pp. 146–157
https://doi.org/10.23939/mmc2020.01.146
Received: November 19, 2019
Revised: May 12, 2020
Accepted: May 13, 2020

Mathematical Modeling and Computing, Vol. 7, No. 1, pp. 146–157 (2020)

Authors:
  1. N. V. Mazuriak
  2. Ya. H. Savula
1
Ivan Franko National University of Lviv
2
Ivan Franko National University of Lviv

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.

multiscale finite element method
advection-diffusion
inhomogeneous medium
  1. Savula Ya.  Numerical analysis of problems of mathematical physics by variational methods.  Lviv, LNU (2004), (in Ukrainian).
  2. Efendiev Y., Hou T.  Multiscale finite element methods. Theory and application.  New York, Springer–Verlag (2009).
  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).
  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).
  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).
  6. Spodar N., Savula Ya.  Computational aspects of multiscale finite element method.  Physico-mathematical modelling and informational technologies. 23, 169–177 (2016), (in Ukrainian).
  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).
  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).
  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).
  10. Rashevskij P.  Course of differential geometry.  Moscow, Leningrad, State publishing house of technical and theoretical literature (1950), (in Russian).