# Emeritus ProfessorAnatolyRuban

Faculty of Natural SciencesDepartment of Mathematics

Emeritus Professor

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### Contact

+44 (0)20 7594 8498a.ruban

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### Location

748Huxley BuildingSouth Kensington Campus

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## Fluid Dynamics 1 - MATH97088

### Aims

This course is an introduction to Fluid Dynamics.  It will be followed by Fluid Dynamics II in the Spring Term.  Fluid Dynamics deals with the motion of liquids and gases. Being a subdivision of Continuum Mechanics fluid dynamics does not deal with individual molecules.  Instead an 'averaged' motion of the medium is of interest.  Fluid dynamics is aimed at predicting the velocity, pressure and temperature fields in flows past rigid bodies.  A theoretician achieves this goal by solving the governing Navier-Stokes equations.  In this course a derivation of the Navier-Stokes equations will be presented, followed by description of various techniques to simplify and solve the equation with the purpose of describing the motion of fluids at different conditions.

To introduce the students to various aspects of Viscous Fluid Dynamics, and to demonstrate the power (and beauty) of modern mathematical methods employed when analysing fluid flows.  This includes the Method of Matched Asymptotic Expansions which was put forward by Prandtl for the purpose of mathematical description of flows with small viscosity.  Now this method is used in all branches of Applied Mathematics.

Lecturer

## Fluid Dynamics 1 - MATH97008

### Aims

This course is an introduction to the Fluid Dynamics.  It will be followed by Fluid Dynamics II in Term 2

Fluid Dynamics deals with the motion of liquids and gases.  Being a subdivision of Continuum Mechanics the fluid dynamics does not deal with individual molecules.  Instead an ‘averaged’ motion of the medium is of interest.  Fluid dynamics is aimed at predicting the velocity, pressure and temperature fields in flows past rigid bodies.  A theoretician achieves this goal by solving the governing Navier-Stokes equations.  In this course a derivation of the Navier-Stokes equations will be presented, followed by description of various techniques to simplify and solve the equation with the purpose of describing the motion of fluids at different conditions.

Aims of this course:

To introduce students to fundamental concepts and notions used in fluid dynamics.  To demonstrate how the governing equations of fluid motion are deduced, paying attention to the restriction on their applicability to real flows.  Then a class of exact solutions to the Navier-Stokes equations will be presented.  This will follow by a discussion of possible simplifications of the Navier-Stokes equations. The main attention will be a wide class of flows that may be treated as Inviscid.  To this category belong, for example, aerodynamic flows.  Students will be introduced to theoretical methods to calculate inviscid flows past aerofoils and other aerodynamic bodies.  They will be shown how the lift force produced by an aircraft wing may be calculated.

Lecturer