Computational Fluid Dynamics for Incompressible Flows

Overview

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COURSE OUTLINE: This is an introductory course on computational fluid dynamics (CFD). This course will primarily cover the basics of computational fluid dynamics starting from the classification of partial differential equations, linear solvers, finite difference method and finite volume method for discretizing Laplace equation, convective-diffusive equation & Navier-Stokes equations. The course will help faculty members, students and researchers in the field to get an overview of the concepts in CFD

Syllabus

Computational Fluid Dynamics for Incompressible Flows: Intro Video.
Lec 1: Applications of CFD.
Lec 2: Basic equations of fluid dynamics and heat transfer.
Lec 3: Initial and boundary conditions.
Lec 4: System of second-order PDEs.
Lec 5: System of first-order PDEs.
Lec 6: Finite difference by Taylor series expansion.
Lec 7: Finite difference by general approximation and polynomials.
Lec 8: Finite difference in non-uniform grid.
Lec 9: Types of error and accuracy of FD solutions.
Lec 10: Finite difference formulations of Elliptic Equations with boundary condition treatment.
Lec 11: Iterative Methods.
Lec 12: Applications.
Lec 13: Linear Solvers.
Lec 14: Finite difference formulations of Parabolic Equations.
Lec 15: Finite difference formulations of Parabolic Equations: Implicit Methods.
Lec 16: Finite difference formulations of Parabolic Equations: Unsteady Two-Dimensional Equation.
Lec 17: Finite difference formulations of Parabolic Equations: Unsteady Three-Dimensional Equation.
Lec 18: Finite difference formulations of the first order wave equation: Explicit Method.
Lec 19: Finite difference formulations of the first order wave equation: Implicit Method.
Lec 20: Von Neumann stability analysis of different schemes for Parabolic equations.
Lec 21: von Neumann stability analysis of different schemes for Parabolic equations.
Lec 22: von Neumann stability analysis of different schemes for Hyperbolic equations.
Lec 23: Modified equation, Artificial viscosity, Numerical diffusion.
Lec 24: Discretization vorticity-stream function equations using FDM.
Lec 25: Boundary conditions for flow problems.
Lec 26: Solutions of vorticity-stream function equations.
Lec 27: Solution of Navier-Stokes Equation using FDM.
Lec 28: Solution of Navier-Stokes Equation using FDM (Continued).
Lec 29: Introduction to finite volume method.
Lec 30: Finite volume discretization of steady diffusion equation.
Lec 31: Finite volume discretization of unsteady diffusion equation.
Lec 32: Finite volume discretization of steady convection- diffusion equation.
Lec 33: Finite volume discretization of unsteady convection- diffusion equation.
Lec 34: Convection Schemes.
Lec 35: Solution of Navier-Stokes Equations using FVM.
Lec 36: Solution of Navier-Stokes Equations using FVM - II.
Lec 37: Boundary Conditions.