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
