Numerical Methods in Fluid Dynamics
( 25 Modules )

Module #1
Introduction to Numerical Methods in Fluid Dynamics
Overview of numerical methods, importance in fluid dynamics, and course objectives

Module #2
Mathematical Preliminaries
Review of vector calculus, differential equations, and linear algebra

Module #3
Governing Equations of Fluid Dynamics
Navier-Stokes equations, conservation laws, and boundary conditions

Module #4
Finite Difference Methods
Introduction to finite difference methods, accuracy, and stability analysis

Module #5
Finite Difference Methods for 1D Problems
Application of finite difference methods to 1D problems, such as Burgers equation

Module #6
Finite Difference Methods for 2D Problems
Application of finite difference methods to 2D problems, such as Poissons equation

Module #7
Finite Element Methods
Introduction to finite element methods, weak forms, and Galerkin methods

Module #8
Finite Element Methods for Fluid Dynamics
Application of finite element methods to fluid dynamics problems, such as Stokes flow

Module #9
Lattice Boltzmann Methods
Introduction to lattice Boltzmann methods, kinetic theory, and lattice Boltzmann equation

Module #10
Lattice Boltzmann Methods for Fluid Dynamics
Application of lattice Boltzmann methods to fluid dynamics problems, such as channel flow

Module #11
Computational Fluid Dynamics (CFD) Software
Overview of commercial and open-source CFD software, such as OpenFOAM and ANSYS Fluent

Module #12
Mesh Generation
Methods for generating meshes, mesh quality, and mesh refinement

Module #13
Numerical Solution of Linear Systems
Methods for solving linear systems, such as Gauss elimination and conjugate gradient method

Module #14
Numerical Solution of Nonlinear Systems
Methods for solving nonlinear systems, such as Newtons method and fixed-point iteration

Module #15
Time-Stepping Methods
Methods for time-stepping, such as Eulers method, Runge-Kutta method, and implicit methods

Module #16
Boundary Conditions and Stability Analysis
Implementation of boundary conditions and stability analysis for numerical methods

Module #17
Validation and Verification
Methods for validating and verifying numerical solutions, including error analysis and uncertainty quantification

Module #18
Case Studies in Fluid Dynamics
Application of numerical methods to specific fluid dynamics problems, such as pipe flow and cavity flow

Module #19
Turbulence Modeling
Introduction to turbulence modeling, Reynolds-averaged Navier-Stokes (RANS) equations, and large eddy simulation (LES)

Module #20
Advanced Topics in Numerical Methods
Advanced topics, such as multigrid methods, immersed boundary methods, and adaptive mesh refinement

Module #21
High-Performance Computing (HPC) for Fluid Dynamics
Introduction to HPC, parallel computing, and GPU acceleration for fluid dynamics simulations

Module #22
Uncertainty Quantification and Sensitivity Analysis
Methods for uncertainty quantification and sensitivity analysis in fluid dynamics simulations

Module #23
Optimization and Design in Fluid Dynamics
Methods for optimization and design in fluid dynamics, including adjoint methods and shape optimization

Module #24
Multiphase and Multiscale Fluid Dynamics
Introduction to multiphase and multiscale fluid dynamics, including interface tracking and lattice Boltzmann methods

Module #25
Course Wrap-Up & Conclusion
Planning next steps in Numerical Methods in Fluid Dynamics career

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Numerical Methods in Fluid Dynamics ( 25 Modules )

Numerical Methods in Fluid Dynamics
( 25 Modules )