Week 3 - Taylor table method and Matlab code
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));…
Arghajit Chakraborty
updated on 29 Jul 2020
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Read more Projects by Arghajit Chakraborty (7)
Week 12 - Validation studies of Symmetry BC vs Wedge BC in OpenFOAM vs Analytical H.P equation
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…
27 Aug 2021 03:46 AM IST
Week 9 - FVM Literature Review
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.…
25 Aug 2021 07:45 PM IST
Week 11 - Simulation of Flow through a pipe in OpenFoam
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…
10 Feb 2021 06:02 AM IST
Week 8 - BlockMesh Drill down challenge
blockMeshDict: Case1: /*--------------------------------*- C++ -*----------------------------------*\ ========= | \\ / F ield | OpenFOAM: The Open Source CFD Toolbox \\ / O peration | Website: https://openfoam.org \\ / A nd | Version: 8 \\/ M anipulation | \*---------------------------------------------------------------------------*/…
05 Jan 2021 11:34 PM IST
Week 7 - Simulation of a 1D Super-sonic nozzle flow simulation using Macormack Method
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)…
31 Aug 2020 05:42 PM IST
Week 5 - Mid term project - Solving the steady and unsteady 2D heat conduction problem
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…
18 Aug 2020 06:04 PM IST
Week 3 - Taylor table method and Matlab code
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));…
29 Jul 2020 11:28 PM IST