Question Derive the following 4th order approximations of the second-order derivative.  1. Central difference 2. Skewed right-sided difference 3. Skewed left-sided difference After deriving these schemes, prove that your skewed schemes are fourth-order accurate i.e the thumb rule given in HINT (ii).  Once you…

Question In part 1, you had computed the first, second and fourth order approximations for a given value of x and dx. For this program you need to do the following. 1. For a range of dx, plot the first order, second and fourth order error. dx range = [pi/4000,pi/40,20]  2. Make sure that you plot dx vs error in a…

Question Write a program that compares the first, second and fourth order approximations of the first derivative against the analytical or exact derivative. 1. The function that you will compute if f(x) = sin(x)/x^3 2. You will compute the first derivative at x = pi/3 for dx = pi/30. 2a. You will compute the derivative…

Aim To solve the 2D heat conduction equation by using the point iterative techniques using the methods like Jacobi, Gauss-seidel, Successive over-relaxation for both implicit and explicit schemes.   Inputs and boundary conditions Domain is assumed to be a shape of a square of lenght 1m. No. of nodes at x and y direction…

Question Consider the following system of matrices.Coefficient Matrix, A=[5 1 2 ; -3 9 4; 1 2 -7] Solution Matrix, X=[x1;x2;x3] Residual Matrix, B=[10 -14 33]   EXPECTED RESULTS :  Solve the system of matrices using Jacobi, Gauss-seidel and SOR methods. Compute the Iteration Matrix for the above mentioned methods…

Aim To simulate the isentropic flow through a quasi 1D subsonic-supersonic nozzle. To derive the conservation and non-conservation forms of the governing equations and sovle them using the MacCormack's technique. To plot the distribution of primitive variables, mass flow rate through the nozzle and time-wise variations…

Simulate an incompressible-laminar-viscous flow through the backward facing step geometry Case 1 - Simulate the flow without using any grading factor (i.e., GF = 1) Case 2 - Simulate the flow with grading factor of 0.2. The cells should be finer near the walls (including the step wall).