REPORT – Deriving 4th order approximation of a 2nd order derivative using the Taylor method AIM Derive the following 4th order approximations of the second-order derivative. Central difference Skewed right-sided difference Skewed left-sided difference OBJECTIVE After deriving these schemes, Prove that the skewed…

REPORT – SOLVING THE STEADY AND UNSTEADY 2D HEAT CONDUCTION PROBLEM AIM Steady-State Analysis and Transient State Analysis OBJECTIVE Solve the 2D heat conduction equation by using the point iterative techniques. Implement the following methods for solving implicit equations; Jacobi Gauss – seidel Successive…

REPORT  FVM Literature Review OBJECTIVE What is the Finite Volume Method (FVM)? Major differences between FDM & FVM. Describe the need for the interpolation schemes and flux limiters in FVM. Explain with an example of a 1D linear heat conduction equation. DESCRIPTION FINITE VOLUME METHOD The finite volume method is a widely…

REPORT  1D Supersonic nozzle flow simulation using Macormack Method To simulate the isentropic flow through a Quasi 1D subsonic-supersonic nozzle. Derive both the conservation and non-conservation forms of the governing equations and solve them using MacCormack’s technique. To determine the steady-state temperature distribution…