Deriving the fourth-order  approximation for second order derivative  1. Central Differencing Approximation  Now here p = 4    (Order of approximation)   and         q = 2    (Order of Derivative) The number of grid points in Central Differencing is…

1. Solving Steady State Heat conduction Equation  The Steady State Heat conduction Equation in 2-D form is given as    `(del^2T)/(delx^2)+(del^2T)/(dely^2) = 0`-------------(1)   Where T = Temperature in (K) and x,y are the space co-ordinates  Now we need to discretise Equation (1), So we use Taylor's…

AIM: To analyse a  Quasi 1-D flow through a subsonic Convergent Divergent Nozzle using the Conservative and Non-Conservative form of the Governing Equations and Solving them using the MacCormack Method.  ASSUMPTIONS: The Flow is Isentropic Flow along X direction. The effects due to gravitational Force and Viscous…

Problem Statement: To Simulate the incompressible-Laminar Viscous Flow of a Fluid through a Backward facing Step Geometry. We have to do it as per the Following Cases  Case 1: Simulation of Flow without using any grading Factor (i.e G.F = 1) Case 2: Simulation of Flow with G.F = 0.2 and the cell should be finer near…

The Finite Volume Method: The FVM(Finite Volume Method) other than the FDM(Finite Difference Method) is a Method we use to discretise the Governing Equations (Partial Differential Equations) into Algebraic Equations and to solve these Equations all over the Fluid Domain and thus solve the Fluid Flow. FDM and FVM discretise…

Problem Statement: To simulate an axis-symmeteric flow through a pipe by applying wedge boundary conditions, the flow is Laminar and has an inlet Reynolds number as Re = 2100 and we have to validate the steady flow velocity distribution of a fully developed Laminar Flow with the velocity distribution obtained by solving…

Problem Statement: Comparing the Velocity profiles of a Laminar Viscous Flow through a pipe for Wedge BC and Symmetry BC with the Analytical Results obtained by Solving Hagen-Poiseuille's Equations.  The Reynolds Number for the Flow is given by Re = 2100  The Hagen Poiseuille's Equation for solving velocity profile…

Aim: Modifying a existing solver to solve a scalar transport Equation for a scalar quantity "s".  Summary: We modify the icoFoam solver which originally solves the Equation for transient incompressible flow using PISO algorithm, a pressure-velocity coupling algorithm to give us the variation of Pressure and Velocity…

The LaTex code for the report is given as \documentclass[12pt]{report} \usepackage{parskip} \usepackage{graphicx} \usepackage{caption} \usepackage{amsmath,amssymb,amsthm} \usepackage[utf8]{inputenc} \usepackage[a4paper, total={6.5in, 9.8in}]{geometry} \title{Creating a custom IOobject in VScode} \author{Kawal Thakur} \usepackage{sectsty}…

\documentclass[12pt]{report} \usepackage{parskip} \usepackage{hyperref} \usepackage{graphicx} \usepackage{caption} \usepackage{amsmath,amssymb,amsthm} %\usepackage{physics} \usepackage[utf8]{inputenc} \usepackage[a4paper, total={6.5in, 9.8in}]{geometry} \title{Adding a temperature dictionary to the incompressible icoFoam…

\documentclass[12pt]{report} \usepackage{parskip} \usepackage{hyperref} \usepackage{graphicx} \usepackage{caption} \usepackage{amsmath,amssymb,amsthm} %\usepackage{physics} \usepackage[utf8]{inputenc} \usepackage[a4paper, total={6.5in, 9.8in}]{geometry} \title{Running OpenFoam cases to compare the discretisation Schemes}…