Syllabus
* Derivation of equations describing the flow:
Basic concepts of gas dynamics, description of the flow, the transport theorem, fundamental physical laws (the law of conservation of mass, the law of conservation of momentum and the law of conservation of energy) and their formulation in the form of differential equations, constitutive and rheological relations, the Euler and Navier-Stokes equations, thermodynamical laws.
* Formulation of boundary value problems of the theory of elasticity:
The stress tensor, the equations for the equilibrium state, the finite strain tensor, the small strain tensor, generalized Hooke's law, the Lame equations, the Beltrami-Michell equations, basic boundary value problems of elasticity.
* Modelling of inviscid flow:
Inviscid irrotational flow described by the velocity potential, existence of potential, Bernoulli equation, full potential equation, boundary conditions, flow around an airfoil, force acting on the airfoil.
* Modelling of porous media flow:
Conservation of mass in flow with sources, Darcy law, permeability, equation for pressure, formulation of porous media flow with discontinuous permeability, weak formulation of elliptic equations with discontinuous coefficients.
* Transport proceses:
Equation describing the transport of alloys in flow, convection-diffusion processes, applications in ekology.
Annotation
The course is devoted to derivations of equations describing complex technical and physical structures and processes. Recommended for bachelor's program in General Mathematics, specialization Mathematical Modelling and Numerical Analysis.