Introduction: Vector and scalar fields in Cartesian, cylindrical and spherical coordinates. Ordinary differential equations. Flow visualization: Streamlines, streamtubes, pathlines, streaklines, timelines. Strain rate tensor. Flux integrals and applications. Norms. Iterative methods for systems of linear and nonlinear equations. Banach fixed-point theorem. Newton method and Gradient method.
Partial differential equations (PDE). Classification of Partial differential equations. Boundary-value problems. Solving PDE using Fourier series and some analytical methods. Finite volume and finite difference numerical methods for PDE. Consistence, convergence and stability of solution methods. Fourier-von Neumann stability analysis. Lax equivalence theorem. Heat equation and diffusion equation in 3D. Laplace equation. Wave equation. Vibrating strings and membranes. Conservation of mass - The continuity equation.The Reynolds Transport equation. Stress tensor and Cauchy’s equation.The Navier-Stokes Equations. Turbulence and its modeling. Reynolds-averaged Navier-Stokes equations. The finite volume method for convection-diffusion problems.The finite volume method for some unsteady flows.
SIMPLE, SIMPLER, SIMPLEC and PISO algorithm.