Lectures related to Numerical Flow Simulation: Discretization Methods & Fluid Interfaces

Numerical Methods for Boundary Value Problems

Covers numerical methods for solving boundary value problems using finite difference, FFT, and finite element methods.

Focuses on numerical modelling of atmospheric processes to predict weather and climate phenomena, covering key concepts and methods.

Other Topics: Techniques for Fluid Interfaces

Explores numerical methods for fluid dynamics and techniques for handling fluid interfaces.

Continuum Mechanics: Conservation Laws and Kinematics

Introduces continuum mechanics, focusing on conservation laws and kinematics for continuous media.

Verification and validation

Covers the verification and validation process in numerical flow simulation, ensuring credibility of simulation outcomes.

Numerical Differentiation: Part 1

Covers numerical differentiation, forward differences, Taylor's expansion, Big O notation, and error minimization.

Numerical Methods: Boundary Value Problems

Covers numerical methods for solving boundary value problems, including applications with the Fast Fourier transform (FFT) and de-noising data.

System of ODEs

Explores numerical methods for solving ODE systems, stability regions, and absolute stability importance.

Wave Equations: Vibrating String

Explores the wave equation for a vibrating string and its numerical solution using finite difference formulas and the Newmark scheme in MATLAB/GNU Octave.

Numerical Methods: Euler and Crank-Nicolson

Covers Euler and Crank-Nicolson methods for solving differential equations.

Boundary Value Problems: Numerical Methods

Covers the motivation and examples of boundary value problems, the finite difference method, and the approximation of local derivatives.

Thomas algorithm, accuracy of direct methods

Explores the Thomas algorithm for tridiagonal systems and the accuracy of direct methods in numerical computations.

Numerical Methods: Boundary Value Problems

Explores boundary value problems, finite difference method, and Joule heating examples in 1D.

Finite Element Modeling: Introduction

Introduces finite element modeling for numerical solutions to complex problems.

Numerical Flow Simulation: Methods and Applications

Explores numerical methods for flow simulation, including finite element, spectral, particle, and lattice Boltzmann methods.

Numerical Methods: Euler Schemes

Focuses on Euler schemes for numerical approximation of forces and velocities.

Finite Difference Method: Approximating Derivatives and Equations

Introduces the finite difference method for approximating derivatives and solving differential equations in practical applications.

Numerical Differentiation: Backward and Central Differences

Explores backward and central differences for numerical differentiation, analyzing their properties and error analysis.

Finite Difference Grids

Explains finite difference grids for computing solutions of elastic membranes using Laplace's equation and numerical methods.

Finite Differences Formulas: Error Analysis

Explores finite differences formulas, error analysis, and numerical experiments in computational mathematics.