Lectures related to Diffusion Equations: Green's Function Approach

Covers the foundations of fluid mechanics, focusing on flow problem descriptions and solutions.

Explores transient flow in porous media, covering governing equations, stability conditions, and numerical methods.

Explores the Poisson problem with Neumann boundary conditions and periodic boundary conditions in mathematical modeling and fluid dynamics.

Explores turbulence characteristics, simulation methods, and modeling challenges, providing guidelines for choosing and validating turbulence models.

Covers the fundamentals of two-phase flow and heat transfer phenomena.

Covers the differential approach to fluid dynamics, focusing on conservation laws and the Cauchy stress tensor.

Covers the Cauchy problem in differential equations, focusing on initial conditions and their impact on solution uniqueness.

Explores boundary conditions, basis functions, and PDE solutions using Fourier and Bessel series.

Explores transport effects in heterogeneous catalysis, including molecular diffusion and Knudsen diffusion in different types of pores.

Discusses Newton's 2nd Law in fluid dynamics and incompressible Newtonian fluids.

Explores diffusion from a macroscopic perspective, emphasizing the derivation of the diffusion equation through mass conservation and fixed flux law.

Discusses the numerical analysis of pollutant transport equations and their applications in environmental modeling.

Explores the Poisson problem with periodic boundary conditions and the application of Fourier series in mathematical modeling.

Covers the analysis of incompressible fluid flow and numerical solutions in fluid dynamics.

Explains the Laplace equation in 2D with mixed boundary conditions.

Covers the numerical simulation workflow for fluid dynamics, focusing on boundary conditions and their importance for solution convergence.

Covers the basics of continuum mechanics, including forces transmission, energy conservation, and body motion geometry.

Provides an overview of the mathematical analysis of vibrating strings using Fourier series and Laplace transforms.

Explores diffusion in incompressible fluid mechanics, covering continuum description, Fick's law, and steady-state solutions.