DOI: https://doi.org/10.15588/1607-3274-2018-2-3

### METHOD OF NUMERICAL ANALYSIS OF THE PROBLEM OF MASS TRANSFER OF A CYLINDRICAL BODY WITH THE UNIFORM TRANSLATIONAL FLOW

S. N. Lamtyugova, M. V. Sidorov, I. V. Sytnykova

#### Abstract

Context. The problem of mass transfer of a cylindrical body with a uniform translational flow of a viscous incompressible fluid is
examined in the paper.
Objective. The purpose of this work is to develop a new method for numerical analysis of the problem of mass transfer of a cylindrical
body with a uniform translational flow, which based on the joint application of the R-functions structural method and the Galerkin
projection method.
Method. In general case, the problem of stationary mass transfer of a cylindrical body with a viscous incompressible fluid flow is reduced
to the solution of the equation of hydrodynamic flow passing a surface and an equation for concentration with corresponding boundary
conditions on the surface of the body and far away from it. The geometry of the area, and also the boundary conditions (including the
condition at infinity) may be taken into account precisely by using the constructive apparatus of the R-functions theory by V. L. Rvachev,
the Academician of Ukrainian National Academy of Sciences. In this study, a complete structure of the solution of a linear boundary value
problem for the concentration that exactly satisfies the boundary conditions on the boundary and condition at infinity is constructed on the basis of the R-functions theory methods, and this made it possible to lead the tasks in the infinite domain to tasks in the finite domain. To
solve the linear problem for concentration the numerical algorithm on the basis of Galerkin method is developed.
Results. The computational experiment for the problem of the flow past circular and elliptical cylinders at various Reynolds and Peclet
numbers was carried out.
Conclusions. The conducted experiments have confirmed the efficiency of the proposed method of numerical analysis of the problem
of mass transfer of a cylindrical body with a uniform translational flow, based on the joint application of the R-functions structural method
and Galerkin projection method. The prospects for the further research may be to use the developed method for the implementation of
iterative methods for solving the task of nonlinear mass transfer, semi-discrete and projection methods for solving the non-stationary
tasks, as well as in solving the tasks of optimal management of relevant technological processes.

#### Keywords

flow task; stationary flow; viscous fluid; stream function; mass transfer; concentration function; R-functions method; Galerkin method.

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