The matlab code  clear all close all clc % matrices to solve variables for skewed right side difference B1 = [ 1 1 1 1 1 1 ; 0 1 2 3 4 5 ; 0 1 4 9 16 25 ; 0 1 8 27 64 125 ;0 1 16 81 256 625 ; 0 1 32 243 1024 3125] A1 = [0 ; 0;2;0;0;0] X1 = inv(B1)*A1; a1 = X1(1); b1 = X1(2); c1 = X1(3); d1 = X1(4); e1 = X1(5); g1…

Matlab code for solving the above problem in steady state clear all close all clc %Inital conditions nx1 = 10; nx2 = 10 ; x = linspace(0,1,nx2); y = linspace(0,1,nx1); error = 9e9; error1 = 9e9; error2 = 9e9; tol = 1e-4; dx = x(2)-x(1); dy = y(2)-y(1); [ xx yy ] = meshgrid(x,y); p =1; while(p<4) if(p==1) %Boundary conditions…

Here we are computing Distribution of temperature , velocity , Density, and mass flow rates in quasi 1D isentropic subsonic and super sonic flows using two forms of governing solutions by MacCormack's technique. The two forms of governing equations are  1. Non conservative technique  2. Conservative technique …

Fintite Volume Method : 1. It is one of the descretization methods to solve the partial differential equations in computer . 2.In Finite volume method we descretise using a volume , The volume might be of any shape . 3. In that volume everything is conserved i.e momentum , Energy , Mass are conserved . 4. In Finite volume…

First we need to know which problem we are going to solve and we need to identify which tutorial in openfoam is useful to solve our problem. For that we need to grind through all the tutorials available and identify the required one  The above problem is to solve incompressible laminar viscous flow through a backward…

Hagen-Poiseullie's equation is a physical law used to calculate the pressure drop across a pipe of uniform crossection  through which there is laminar flow of a viscous , incompressible, Newtonian fluid Hagen-Poiseullies equation is  `Deltap = (32* mu*l*V_(avg))/(d^2)`  `nu = mu/rho` `V_(avg) = (Re*mu)/(rho*d)`…

In this challenge we are going to validate the results we get from simulating the flow for two different boundary conditions  1. Wedge boundary conditions  2. Symmetry bounday conditions  The quantities we are going to validate are  1.Hydro dynamic length  2.Fully developed velocity profile …