Discretisation basics

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…

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…

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).

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 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…

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…