Introduction to Continuum Dynamics

Garant předmětu:

Radek Fučík, Pavel Strachota

Lecturer:

Tutor:

Radek Fučík, Pavel Strachota

Supervisor:

Department of Mathematics

Synopsis:

The course provides a rigorous introduction to the mathematical description of continuum dynamics. In the first part, the necessary mathematical tools are summarized, focusing on vector and tensor calculus, differential forms, and integration on manifolds. Next, the fundamental concepts such as several deformation tensors and the substantial (material) derivative are defined. They are used subsequently in the derivation of the conservation laws of mass, momentum and energy in both integral and differential forms. The conservation laws are further adapted to the specific cases of viscous and inviscid fluid and linear/nonlinear elastic body.

Requirements:

Basic courses in calculus, linear algebra, theoretical physics and differential equations (according lectures at CTU in Prague 01DIFR, 01LA1, 01LAA2, 01MA1, 01MAA2, 01MAA3, 02TEF1).

Syllabus of lectures:

1. Mathematical tools: vector and tensor calculus, differential forms, integration on manifolds

2. Fundamental concepts of continuum mechanics: motion and deformation of bodies, strain tensors and small strain

tensor, decomposition of strain, rotations, substantial derivative of scalars and vectors

3. Conservation laws: conservation of mass, conservation of linear and angular momentum, conservation of total and

internal energy

4. Constitutive relations: inviscid fluid, viscous fluid, nonlinear and linear elastic body, N

ewtonian and non-

Newtonian fluids

5. Some flow types and their mathematical specifics (compressible and incompressible flow, laminar and turbulent flow,

irrotational flow, multiphase flow, flow in porous media)

6. Analytical solutions of selected flow problems

Syllabus of tutorials:

Study Objective:

Knowledge:

The basic principles of continuum mechanics description. Conservation laws for mass, momentum, angular momentum, and energy. Constitutive equations for viscous and inviscid fluid. Constitutive relations for linear and nonlinear elastic body.

Abilities:

Derivation of basic conservation laws. Derivation of the constitutive relations for the case of fluid or elastic body.

Study materials:

Key references:

[1] J. N. Reddy, Principles of Continuum Mechanics: Conservation and Balance Laws with Applications. Cambridge

University Press, 2017.

[2] Y. A. Cengel, J. M. Cimbala, Fluid Mechanics: Fundamentals and Applications (4th ed.), McGraw-Hill Education,

2017.

[3] J. Tu, Jiyuan, G-H. Yeoh, and C. Liu. Computational Fluid Dynamics: A Practical Approach. Butterworth-

Heinemann, 2018.

[4] I. Štoll, J. Tolar, I. Jex. Klasická teoretická fyzika. Charles University in Prague, Karolinum Press, 2017.

Recommended references:

[5] J. D. Anderson, Jr., Computational Fluid Dynamics: The Basics with Applications. McGraw-Hill, 1995.

[6] M. Gurtin, An Introduction to Continuum Mechanics. Vol. 158. Academic Press, 1981.

[7] F. Maršík, F. Termodynamika kontinua. Academia, 1999.

Note:

Time-table for winter semester 2023/2024:

Time-table is not available yet

Time-table for summer semester 2023/2024:

Time-table is not available yet

The course is a part of the following study plans:

• Fyzikální inženýrství - Počítačová fyzika (PS)
• Matematické inženýrství - Matematické modelování (PS)
• Physical Engineering - Computational physics (PS)