Derive the 4th order approximations of the second order derivative using various finite difference schemes .

Aim:   To understand the concept of the genetic algorithm and write code in MATLAB to optimize the stalagmite function and find the global maxima of the function.   Theory:  The stalagmite function is a function with 4 components : 2 sine components in each of the axis direction  2 normal…

Aim:  Perform the linear and cubic fit for a given set of data and then gain insights on the several parameters that can be used to identify a good fit.   Theory:  Curve fitting is the process of constructing a mathematical curve to fit the data points according to some criteria to get a mathematical formula…

Objective : To study the theory behind the various interpolation schemes and the flux limiters in case of the Finite Volume Method.   Why the need for FVM? In advanced CFD approaches with highly unstructured grids, we tend to use a method called as the finite Volume Method ( FVM ). While in the normal discretization…

Aim: To demonstrate the working of an otto cycle and write a MATLAB code to plot the graphs and calculate the thermal efficiency. Theory: The Air-Standard cycles work on the principle that the working medium is air. These cycles gained became more and more popular in the theoretical analysis of an Internal Combustion Engine.…

Aim: To simulate the isentropic quasi 1-D nozzle flow using the MacCormack's Method for both conservative and non-conservative forms of the governing equations and compare the results regarding the primitive variables such as Temperature, Pressure, Density, and Mass Flow rate.   Theory:  Consider a Convergent-Divergent…

Aim: To study the motion of a simple pendulum.   Theory:  The way the pendulum moves depends on Newton's second law of motion. When this second law equation is written for the pendulum, we get a second order Ordinary Differential Equation that describes the position of the "bob" with respect to time.    …

Objective: In this report, we analyze the stability in a Transient Problem of the 2-D Heat Conduction model.   Theory :  The only difference between the steady-state and transient state analysis is that in the study state the solution will not change with time. However, in the transient systems the solution changes…

In this report, the emphasis has been laid about solving the 2-D heat conduction equation ( Steady State and Transient State) using several iterative methods. The methods implemented are :                                      …

Objective:  In this report, we shall look at the simulation of a 2-R robotic arm using MATLAB.   Theory: A robotic arm is a type of mechanical with similar functions to a human arm; the arm may be the sum total of the mechanism or may be part of a more complex robot. The links of such a manipulator…

In this report, the emphasis has been laid about solving the system of linear equations using several iterative methods. The methods implemented are :                                         1.) Jacobi      …

In this project we are going to derive the 4th order approximations of the second-order derivative using the following schemes :  1.)  Central Differencing 2.)  Skewed right-sided difference 3.)  Skewed left-sided difference  The analytical function for which we will derive these schemes is f(x)…

Here we are required to compute the First Numerical and Analytical derivatives.   Definition of Analytical Derivative:  It can be referred to as the exact derivative i.e. the exact value of the derivative of the function at a given point. Definition of Numerical Derivative:  It can be referred to as the…

Here we need to solve the 1-D linear convection Equation which is given by:   `frac(partialu)(partialt) + cfrac(partialu)(partialx) =0`   Now to solve it numerically, we need to implement some differencing schemes of the numerical techniques to discretize the equation.   The discretization for the first-order…

Here we need to solve the 1-D linear convection Equation which is given by: `frac(partialu)(partialt) + cfrac(partialu)(partialx) =0`   Now to solve it numerically, we need to implement some finite differencing schemes of the numerical techniques to discretize the governing equation. The discretization for the first-order…

In the theory of the Stoichiometric combustion assuming when the fuel and air mix, the products produced are only CO2, H2O, and N2.                                                     …