Comparing the first, second, and fourth-order approximations of the first order derivative against the analytical or exact derivative using MATLAB

PROBLEM SPECIFICATION: Simulate the flow over a cylinder and explain the phenomenon of Kármán Vortex Street using ANSYS Fluent.    PART-I:- Simulate the flow with the steady and unsteady case and calculate the Strouhal Number for Re= 100.  PART-II:- Calculate the coefficient of drag and lift…

PROBLEM SPECIFICATION: For this project, we have created two versions of the T-junction. One of them is longer than the other. Our job is to set up steady-state simulations to compare the mixing effectiveness when the hot inlet temperature is 360C & the Cold inlet is at 190C.  Use the k-epsilon and k-omega SST…

NOTE: This project is the continuation of the last project, "Simulation of Laminar Viscous Flow through a regular Pipe using Wedge Boundary conditions in OpenFOAM and post-processed in ParaView". It is highly recommended to read that project first, to have a better understanding of this one! Problem Specification:…

Problem Specification: Write a program in MATLAB that can generate the computational mesh automatically for any wedge angle (wedge angle should be less than 5 degrees) and grading schemes. For a baseline mesh, show that the velocity profile matches with the Hagen Poiseuille's equation. Show that the velocity profile…

SIMULATION OF LAMINAR FLOW OVER A BACKWARD FACING STEP USING THE icoFoam SOLVER IN OpenFOAM TO SHOW THE EFFECT OF DIFFERENT MESH GRADING FACTOR ON THE SOLUTION PROBLEM SPECIFICATION: Problem Statement: By using the icoFoam solver in OpenFOAM, simulate the flow through a Backward Facing Step, and compare the results for…

SIMULATION OF QUASI-ONE-DIMENSIONAL SUPERSONIC NOZZLE FLOW USING MACCORMACK METHOD PROBLEM SPECIFICATION:- In this project, we will simulate the isentropic flow through a quasi 1D subsonic-supersonic nozzle. We will derive both the conservation and non-conservation forms of the governing equations and solve them using…

  Solving the Steady and Unsteady 2-D Heat Conduction Equation in MATLAB Problem Specification:- Solving the steady-state 2-D heat conduction equation implicitly using point-iterative methods; such as Jacobi, Gauss-Seidel, and Successive Over-Relaxation (SOR). Solving the unsteady (transient)-state 2-D heat conduction…

Stability Analysis for different Iterative Solvers on a System of Linear equations in MATLAB Problem Specification:- Solving the system of linear equations in MATLAB using different iterative solvers and showing: The impact of the spectral radius on the convergence of the solution. The effect of diagonal magnification…

PROBLEM SPECIFICATION Stoichiometric combustion offers an easy way to understand combustion concepts. When fuel and air mix they produce products as co2, co, oh, h2o, no, n2o, and many more. In stoichiometric combustion, we make a simple assumption that the by-products are only co2, h2o, and n2. For a generic alkane fuel,…

PROGRAM IN MATLAB/OCTAVE TO SIMULATE THE PENDULUM MOTION OBJECTIVE:- To write a program in MATLAB/OCTAVE to solve the equation of motion of a simple pendulum (with damping). To simulate the pendulum motion b/w 0-20sec, for angular displacement=0, angular velocity=`3 rad⁄sec`; at time t=0. PROBLEM FORMULATION AND…

Numerical analysis of 1-D Linear Convection equation using MATLAB to show the effect of Time Step Size (dt) on the solution PROBLEM SPECIFICATION:- Assumptions: Domain Length, L=1m. The initial velocity profile is a step function. It is equal to 2m/s between x=0.1 & 0.3, and 1m/s everywhere else. The number of grid…

OBJECTIVE:- Write a program in MATLAB that compares the first, second, and fourth-order approximations of the first derivative against the analytical or exact derivative. For a function, `f(x)=sinx/x^3`; we’ll compute the first derivative at `x=pi/3`; both numerically and analytically. Define…

Derive the following 4th order approximation of the second-order derivative using:- 1. Central difference 2. Skewed right-sided difference 3. Skewed left-sided difference Also, prove that your skewed schemes are fourth-order accurate.  Write a program in Matlab to evaluate the second-order derivative of the analytical…

Numerical analysis of 1-D Linear Convection equation for varying grid points (n) using MATLAB PROBLEM SPECIFICATION:- Assumptions: Domain Length, L=1m. The initial velocity profile is a step function. It is equal to 2m/s between x=0.1 & 0.3, and 1m/s everywhere else. Using first-order forward differencing for the time…