Numerical analysis of the advection-diffusion problems in thin curvilinear channel based on multiscale finite element method

2017;
: pp. 59-68
https://doi.org/10.23939/mmc2017.01.059
Received: June 17, 2017
1
Ivan Franko National University of Lviv
2
Ivan Franko National University of Lviv

The advection-diffusion problem in a thin curvilinear channel is considered. The multiscale finite element method is applied to solving the formulated model problem. It is shown that this method is efficient in the case of sufficiently large Peclet numbers. Numerical examples are presented and analysed.

  1. Savula Ya. Numerical analysis of problems of mathematical physics by variational methods. Lviv, 221 p. (2004).
  2. Efendiev Y., Hou T. Multiscale finite element methods. Theory and application. NY, Springer (Surveys and Tutorials in the Applied Mathematical Sciences), Vol.4, 234 p. (2009).
  3. 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).
  4. Spodar N., Savula Ya. Computational aspects of multiscale finite element method. Physico-mathematical modelling and informational technologies. 23, 169–177 (2016).
  5. Rashevskij P. Course of differential geometry. Moscow, Leningrad (State publishing house of technical and theoretical literature), 3th edition, recycled, 428 p. (1950).
  6. 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).
  7. 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).
Math. Model. Comput. Vol.4, No.1, pp.59-68 (2017)