Code: clc;clear all; close all; syms x func=diff(exp(x)*cos(x),x); df= eval( (subs(diff(func,x),x,pi/3)) ); hvals = linspace(pi/4,pi/400,100); % vector of h values myf=@(x) exp(x).*cos(x); x=pi/3; %Left Skewed approximation to the second derivative-Fourth order f2prime_leftskew_4order = ((45*myf(x))-(154*myf(x-hvals))+(214*myf(x-(2*hvals)))-(156*myf(x-(3*hvals)))+(61*myf(x-(4*hvals)))-(10*myf(x-(5*hvals))))./(12.*(hvals.^2));…

Code for steady state %%%%%%% 2D Heat Equation%%%%%%%%%%%%% %%%%%%% Steady state %%%%%%%%%%%%%%%% %%%%%%%% Arghajit Chakraborty %%%%%%% close all clear all clc %%%%%% nx=21; ny=21; %%%%%% DEFINE BOUNDARY CONDITIONS %%%%%%%% T=300*ones(nx,ny); T(1:nx,1)=400; T(1:nx,end)=800; T(1,1:end)=600; T(end,1:end)=900; %%%%%%%DEFINE…

MATLAB Code MainProgram: %%%%QUASI 1D NOZZLE SIMULATION USING CONSERVATIVE & NON-CONSERVATIVE APPROACH%%%%%% %%%%ARGHAJIT CHAKRABORTY%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% clear all; close all; clc; %%%%%%%%%%%%%%INPUTS%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% L = 3; nodes=[61,31]; for i=1:2 n = nodes(i)…

blockMeshDict:  Case1: /*--------------------------------*- C++ -*----------------------------------*\ ========= | \\ / F ield | OpenFOAM: The Open Source CFD Toolbox \\ / O peration | Website: https://openfoam.org \\ / A nd | Version: 8 \\/ M anipulation | \*---------------------------------------------------------------------------*/…

Abstract In this project, the laminar flow of an incompressible fluid through a pipe is simulated using OpenFOAM. The pressure-drop across the pipe length, the hydrodynamic entry length and the velocity profile are then compared to the analytical values obtained using the Hagen-Poiseuille’s equation. Introduction…

The Finite Volume Method (FVM) The Finite Volume Method (FVM) is an approach to numerically approximate PDEs in their integral form. FVM can be used on all differential equations, which can be written in the divergence form. Thus, the PDE is written using divergence operators and then integrated over the control volume.…

In continuation to the week 11 challenge, in this challenge we continue with the simulation of pipe flow by modeling using wedge angles of 10°, 25° and 45° using both wedge as well as symmetry boundary condition and compare the simulation results with the Hagen–Poiseuille equation.   10° wedge…