Navier-Stokes Equation

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Numerical Analysis of Incompressible Fluid Flow

Covers the software system Channelflow for numerical analysis of incompressible fluid flow in channel geometries, including spectral methods and invariant solutions.

Symmetries and Conservation Laws

Covers symmetries and conservation laws in fluid dynamics, emphasizing the importance of maximizing symmetries in ideal fluid systems.

Poisson Problem: Fourier Transform Approach

Explores solving the Poisson problem using Fourier transform, discussing source terms, boundary conditions, and solution uniqueness.

Fourier Transform: Properties and Applications

Covers the properties and applications of the Fourier transform and its relation to Heisenberg's uncertainty principle.

Fluid Dynamics: Navier-Stokes Equations

Explores fluid dynamics, covering Navier-Stokes equations, momentum conservation, stresses, and dimensional analysis.

Rayleigh Taylor: Normal Mode Expansion

Explores normal mode expansion, Laplace equation solution, and dispersion relation analysis in Rayleigh Taylor instability.

Inviscid Flows: Understanding Fluid Dynamics

Explores inviscid flows, Reynolds number importance, linear deformations, and volume change in fluid dynamics.

Fourier Series: Understanding Coefficients and Periodicity

Explores Fourier series coefficients, periodicity, and series relations.

Viscoelastic Materials: Models and Transformations

Explores viscoelastic materials, transforms, and models in materials science.

Numerical Methods: Boundary Value Problems

Covers numerical methods for solving boundary value problems using Crank-Nicolson and FFT.