Compute Fourth Order approximations for Second Order Derivative of a function using Central Difference and Skewed Right and Left Side Schemes

CONJUGATE HEAT TRANSFER SIMULATION The term conjugate heat transfer is used to describe processes which involve variations of temperature within solids and fluids, due to thermal interaction between the solids and fluids. In this study, fluid flow through an aluminium pipe was considered to perform the Conjugate Heat Transfer…

Transient Simulation of Fluid Flow Through a Throttle Body The aim of this project is to perform a Transient simulation for fluid flow through a throttle body. Converge CFD software is used for the project. For Transient analysis, the throttle body (Butterfly Valve) is moved to an angle of 25 degrees in 2ms and kept in…

Steady-State Simulation of Fluid Flow over a Throttle Body The aim of this project is to perform a steady-state simulation for fluid flow through a throttle body. Converge CFD software is used for the project. For steady-state analysis, the throttle body (Butterfly Valve) is kept in the wide-open position as can been seen…

 Objective:  The objective of this project is to generate the Blockmesh file for a Backward Facing Step using OpemFoam and to simulate flow over the backward-facing step geometry using the icoFoam solver. IcoFoam solver is a transient solver for incompressible, laminar flow for Newtonian FLuids. After the simulation,…

Interpolation Schemes: The approximation of surface and volume integrals may require values of the variables at locations other than the computational nodes of the CV. Values at these locations are obtained using Interpolation Schemes. Some of the commonly used interpolation schemes are: a) Upwind Interpolation Scheme …

INTRODUCTION The aim of this project is to determine the numerical solution of a 1-D Supersonic Nozzle Flow using the Macormack method. Both Conservative, as well as Non-Conservative Approach, are discussed in this project. Although analytically identical, the numerical solution of both these approaches tends to vary a…

Objective: To solve the 2-D Heat Conduction Equation for a Slab using a Steady State and a Transient Approach using Implicit (Iterative Solvers) and Explicit Methods. Types of Iterative Solvers employed: a) Jacobi Method b) Gauss-Siedel Method c) Successive Over-Relaxation Method (SOR)   1) Steady-State Analysis A…

The Linear Convection Equation arises from the Navier-Stokes equation wherein we consider only the convection terms for the x component of the velocity. This equation represents the propagation of a wave without change of shape; the speed of the wave is C. This means that on an axis with the positive direction to the right,…

The Linear Convection Equation arises from the Navier-Stokes equation wherein we consider only the convection terms for the x component of the velocity. This equation represents the propagation of a wave without change of shape; the speed of the wave is C. This means that on an axis with the positive direction to the right,…

Using Taylors table, the following 4th order approximations of the second order derivative have been obtained: 1)  Central difference a(fi-2)+b(fi-1)+c(fi)+d(fi+1)+e(fi+2) where; a=-0.0833; b=1.333; c=-2.5; d=1.333; e=-0.0833   2) Skewed right sided difference a(fi)+b(fi+1)+c(fi+2)+d(fi+3)+e(fi+4) where; a=2.9167;…

Pendulum Motion Analysis The purpose of this project is to solve a second order differential equation which governs the motion of a simple pendulum. The motion of pendulum depends on the Newtons Second Law and follows the second order ODE given by:     In the above equation, g = gravity in m/s2, L = length of…