1 
Name of the course 
Numerical methods for fluid mechanics 
2 
Course of study, specialty 
4, specialty “ Mechanics and mathematical modeling” 
3 
Semester 
7 
4 
number of credits 
4 
5 
Lecturer 
Senior lecturer D. E. Shevchenko 
6 
objectives of the discipline 
to Study the class of problems of fluid motion in a porous medium. Application of the boundary integral equation method and numerical solution methods. Implementation of numerical calculations on the computer. As a result of studying the student should be able to: – give a correct formulation of the boundary value problem for filtration flows. – correctly apply algorithms of numerical solution of problems by the method of integral equations. – implement a numerical algorithm for solving the problem on the computer. – study the convergence of the solution on different grids.

7 
Prerequisites 
Hydrodynamics 
8 
course Contents 
Some problems of the theory of filtrations of a viscous fluid in a porous medium. Theory of potential and the method of boundary integral equations. The main stages of mathematical modeling of filtration processes. 
9 
Recommended reading 
• Arsenin V. Y. Methods of mathematical physics and special functions. Textbook. Moscow: Science. 1984. • Belotserkovsky S. M., Lifanov I. K. Numerical methods in singular integral equations. Moscow: Science. 1985. • Kantorovich L. V., Krylov V. I. Approximate methods of higher analysis. M. – L.: GIFML. 1962. • Verlan A. F., Sizikov V. S. Integral equations: methods, algorithms, programs. Kyiv: Naukova Dumka . 1986. • Derbisova V. A. the Solution of Laplace equations by the method of boundary integral equations. Moscow: Moscow state University. 1985. Ortega D., Reinboldt V. Iterative methods for solving nonlinear systems of equations with many unknowns. Moscow: Science. 1975. • Bernadiner M. G., Entov V. M. Hydrodynamic theory of filtration of anomalous liquids. Moscow: Science. 1975. Danilov V. L., Katz R. M. Hydrodynamic calculations of mutual displacement of liquid in a porous medium. Moscow: Science. 1980. 
10 
methods of teaching 
Lectures, computational practice 
11 
language of instruction 
Russian 
12 
Conditions (requirements) 
– Colloquium – individual tasks 
13 
Form current certification 
Standings 