7 semester

1

Name of the course

Numerical methods for fluid mechanics

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Course of study, specialty

4, specialty  “ Mechanics and mathematical modeling”

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Semester

7

4

number of credits

4

5

Lecturer

Senior lecturer  D. E. Shevchenko  

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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.

 

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Prerequisites

Hydrodynamics

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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.

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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.

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methods of teaching

Lectures, computational practice

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language of instruction

Russian

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Conditions (requirements)

– Colloquium

–  individual tasks

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Form current certification

Standings