Derive the `4^(th)` order approximation of the second-order derivative using central difference scheme let f be the function whose second derivative is approximated at `i^(th)` point using function values at (i-2), (i-1), i, (i+1), (i+2) points. let h be the distance between the consecutive points.  let `(d^2f)/dx^2=a*f_(i-2)+b*f_(i-1)+c*f_i+d*f_(i+1)+e*f_(i+2)+O(h^n)`…

2-D steady state is solved first using the three methods. The three methods are formulated in MATLAB as follows. close all clear all clc % Solving steady state 2D heat conduction equation % Domain is a square of length equal to one n=20; % Number of nodes in x and y direction % Discretization of domain x=linspace(0,1,n);…

In this assignment, unsteady flow through the 1-D convergent-divergent nozzle is explored using MacCormak's technique. The transient flow is solved using finite difference methods on the non-dimensionalized governing equation's conservative and non-conservative forms. Separate functions are created for conservative and…

The appropriate solver for the given flow condition is icoFoam. From the tutorials folder of the OpenFoam, the cavity tutorial which uses icoFoam solver is copied to the run folder. The blockMeshDict file is edited as below according to the following configuration.    blockMeshDict file /*--------------------------------*-…