AIM  To model and create the animation of a simple pendulum-bob system with damping whose motion is described by the 2nd order ODE -  `(d^2theta)/dt^2+b/m*(d theta)/dt+g/l*sintheta=0` where  theta - angular displacement of the bob from the mean position d theta/dt - angular velocity of the bob t - time m…

AIM:- To identify the maximum value of the stalagmite function using the inbuilt MATLAB genetic algorithm function while also studying the behavior of the genetic algorithm during 3 different cases: Unbounded search-space. Bounded search-space. Increased generated population space.   INTRODUCTION:- Stalagmite function…

 AIM:- To develop a program that will parse the NASA Thermodynamic data file and calculate the specific heat, entropy, and enthalpy values for each of the species within their respective local temperature ranges and store their plots with respect to temperature in separate folders. The molecular weight of each of…

AIM:- To calculate the second-order derivative of the following function:- `f(x) = exp(x)*cos(x)` using central difference, skewed forward difference, and skewed backward difference schemes of fourth-order accuracy. THEORY:- The formula for the discretized derivative in each of the schemes is obtained using the Taylor…

AIM:- To perform transient and steady-state analysis of temperature evolution for a 2D domain with the given boundary conditions: Top Boundary = 600 K Bottom Boundary = 900 K Left Boundary = 400 K Right Boundary = 800 K And to compare the explicit and implicit methods of Jacobi, Gauss-Seidel, and Successive Over-Relaxation…

AIM:- To use the MacCormack method to solve the 1-dimensional convergent-divergent nozzle flow problem with the initial conditions provided for both conservative and non-conservative forms of the governing equations.   THEORY:-  A convergent-divergent nozzle is a nozzle that has a decreasing (convergent) area…

AIM:- To use OpenFoam to simulate incompressible-viscous-laminar flow through a backward-facing step with the mesh being created using blockMesh. The effect of the grading factor is also analysed.   THEORY:- OpenFoam is an open-source CFD software that uses C++ code and blockMesh is a mesh generator in OpenFoam. The…

  Finite Volume Method (FVM) is a discretization method used to convert integral forms of governing equations into algebraic equations. This method is inherently conservative due to the use of the integral forms of the equations.   The properties of the discretization method required for the numerical results…

AIM:- To simulate laminar-incompressible flow through a pipe using OpenFOAM using axisymmetric wedge boundary condition and MATLAB and validate with results obtained from Hagen-Poiseulle equation for fully developed flow. MATLAB is used to automate the generation of the blockMeshDict file taking inputs like pipe diameter,…

AIM:- To compare between the numerical results obtained for incompressible, laminar pipe flow using OpenFOAM with the wedge and symmetry boundary conditions and also to compare the results with the analytical results based on the Hagen-Poiseulle equation. The numerical simulation is done for portions/wedges of the pipe…