Classification of Partial Differential Equations; Classification of system of first order PDE’s; Classification of system of second order PDE’s; Boundary conditions; consistency, stability and convergence of FDE; Lax’s equivalence theorem. Finite difference approximations to partial derivatives for equally spaced grid points and unequally spaced grid points. Methods to solve Parabolic partial differential equations, Elliptic and Hyperbolic partial differential equations and stability analysis; Vorticity Stream function formulation of the Navier-Stokes equations, Finite difference methods for steady, viscous incompressible N-S equations: Flow in a lid driven cavity, Viscous flow past a circular cylinder, flow past a sphere. Line Gauss-Seidal, Point Gauss Seidal , SOR schemes, Finite difference applications in Heat conduction and convection; Discussion on first, second and higher order accurate methods. Higher order compact schemes to Navier Stokes equations. |