Introduction to Numerical Methods in Engineering:
Finite Element Methods Overview: Introduction: Historical background, basic concept of the finite element method, comparison with finite difference method; 1-D Applications in heat transfer, fluid mechanics and solid mechanics. Finite element analysis of 2-D problems: numerical integration.
Introduction to Computational Fluid Dynamics:
Basic equations of Fluid Dynamics: General form of a conservation law; Equation of mass conservation; Conservation law of momentum; Conservation equation of energy. Mathematical nature of PDEs and flow equations.
Basic Discretization techniques: Finite Difference Method (FDM); The Finite Volume Method (FVM). Analysis and Application of Numerical Schemes: Consistency; Stability; Convergence; Fourier or von Neumann stability analysis; Modified equation; Application of FDM to wave, Heat, Laplace and Burgers equations.
Integration methods for systems of ODEs: Linear multi-step methods; Predictorcorrector schemes; The Runge-Kutta schemes.
Numerical solution of the incompressible Navier-Stokes equations: Stream function-vorticity formulation; Primitive variable formulation; Pressure correction techniques like SIMPLE method; Lid-driven cavity flow.