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# Computational Fluid Dynamics for Incompressible Flows

## 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.

### Taught by

NPTEL IIT Guwahati

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