Week 3 - Solving second order ODEs

Aim: The aim of this project is as follows: To discuss about the about the different CFD models that are based on the mathematical analysis of Rayleigh Taylor instability. Perform three different cases of CFD simulation of Rayleigh Taylor instability using Ansys Fluent. Discuss about Atwood number and how it affects the…

Aim: To simulate a conjugate heat transfer analysis in an exhaust port. Objectives: To set the mesh for exhaust port geometry with the appropriate y+ considerations and it is a conforming mesh between the solid and fluid components. To set up the test case in Ansys Fluent with appropriate boundary condition, run the solution…

Aim: To simulate an external flow over an Ahmed Body in Ansys fluent. Objectives: To use the split body function in Ansys SpaceClaim to get the required symmetrical geometry of the Ahmed body along its length. Use appropriate enclosures around the Ahmed Body geometry to get the required mesh quality that enables proper…

https://skill-lync.com/projects/to-study-the-flow-over-a-cylinder-and-von-karman-vortex-street-in-ansys-fluent   The above link leads to the project file that solves for the given assignment.

Aim: To simulate the flow over a cylinder in Ansys Fluent and study the phenomenon of Von Karman street. Objectives: To simulate the flow over the cylinder in Ansys Fluent for the case of Reynolds number equal to 100. To calculate the Strouhal number for the case of Reynolds number equal to 100. Calculate the drag and…

Aim: To set up steady-state simulations of mixing-tee in ANSYS-Fluent and compare the mixing effectiveness in different cases. Objectives: To set up steady-state simulations for the following cases: Short length mixing tee with 36-degree Celsius inlet velocity at 3m/s and momentum ratios for the other inlet is 2 and 4…

https://skill-lync.com/projects/simulation-of-flow-through-a-pipe-in-openfoam-using-the-symmetry-boundary-conditionThe above link leads to the project that solves for the given assignment.

Aim: To simulate an axis-symmetric flow through a pipe in OpenFOAM using the Wedge boundary condition. Objectives: To write a code in MATLAB to auto-generate a fully functional blockMeshDict file that takes inputs of pipe length, diameter and wedge angle. To calculate the flow variables like the hydrodynamic length…

Aim: To simulate an axis-symmetric flow through a pipe in OpenFOAM using the Wedge boundary condition. Objectives: To write a code in MATLAB to auto-generate a fully functional blockMeshDict file that takes inputs of pipe length, diameter and wedge angle. To calculate the flow variables like the hydrodynamic length…

Finite Volume Method: The Finite Volume Method (FVM for short) is used to evaluate elliptic, parabolic, or hyperbolic partial differential equations, based on the conservation laws. Just like the Finite Difference Method (FDM) and the Finite Element Method (FEM), FVM also evaluates the variables at discrete locations of…

Aim: To simulate the isentropic flow through a quasi 1D subsonic-supersonic nozzle in MATLAB. Objectives: To derive the conservative and non-conservative forms of the governing equations for the given problem statement. Write a code in MATLAB to solve the equations using MacCormack’s technique. Generate steady-state…

Aim: To simulate the backward facing step in OpenFOAM. Objectives:  To simulate an incompressible-laminar-viscous flow through a backward facing step. Create Geometry and Mesh according to the given specifications for the simulation. Define the appropriate boundary conditions in the Geometry. To simulate the…

Aim: To simulate the backward facing step in OpenFOAM. Objectives:  To simulate an incompressible-laminar-viscous flow through a backward facing step. Create Geometry and Mesh according to the given specifications for the simulation. Define the appropriate boundary conditions in the Geometry. To simulate the…

Aim: To solve for the given set of linear equations using iterative methods and study the convergence rate by varying Spectral Radius. Objectives:  Arrange the given set of linear equations into a system of Matrices. Solve the system of Matrices using Jacobi, Gauss-Seidel and SOR methods. Calculate the Iteration…

Aim: To run a stability analysis in an unsteady state problem definition. Objectives:  To choose a well-defined problem that is solved using unsteady-state methods. To define the stability criteria for the given problem. To demonstrate the conditions at which the solution is stable and unstable. Problem definition:…

Aim: To compare the number of iterations taken to achieve convergence (convergence rate) between Steady-state and Transient analysis. Objectives: To pick a problem that is to be solved by both Steady-state and Transient methods. Solve for the given problem in both Steady-state and Transient methods. Compare the convergence…

Aim: To solve for the 2D heat conduction equation in Steady-state and Transient state in explicit and implicit methods using the iterative techniques. Objectives:  To write a code in MATLAB to solve for the 2D heat conduction equation in Steady-state for the given boundary conditions using the point iterative techniques.…

Aim: To write a code in MATLAB that demonstrates the Numerical solution for the One-Dimensional Linear Convection Equation.   Objectives: To solve for the following One-Dimensional Linear Convection Equation using Numerical Solutions:`(∂u)/(∂t)+c(∂u)/(∂x)=0` The solution is to be calculated using…

Aim: To write a code in MATLAB that demonstrates the Numerical solution for the One-Dimensional Linear Convection Equation.   Objectives: To solve for the following One-Dimensional Linear Convection Equation using Numerical Solutions:`(∂u)/(∂t)+c(∂u)/(∂x)=0` The solution is to be calculated using…

Aim: To write a code in MATLAB that demonstrates the Numerical solution for the One-Dimensional Linear Convection Equation.   Objectives: To solve for the following One-Dimensional Linear Convection Equation using Numerical Solutions:`(∂u)/(∂t)+c(∂u)/(∂x)=0` The solution is to be calculated using…

Aim: To write a code in MATLAB to get the 4th order approximation of the 2nd order derivative of the given function.   Objectives:  To derive the 4th order approximation of the 2nd order derivative for the function: `f(x)=e^xcos x` The 2nd order derivative for the given function is to be found using central difference,…

Aim: To write a program in MATLAB that compares the first, second and fourth order approximations of the first derivative for a range of values of dx. Objectives: To write a program in MATLAB that computes the derivative of fx if fx=sin x ∕x3. The first derivative is to be computed at x = pi for dx has a range of values…

Aim: To write a program in MATLAB that compares the first, second and fourth order approximations of the first derivative against the analytical or the exact derivative. Objectives: To write a program in MATLAB that computes the derivative of fx if fx=sin x ∕x3. The first derivative is to be computed at x = pi for dx =…

Please find the link below that leads to the project file for the Rankine Cycle simulator.https://skill-lync.com/projects/rankine-cycle-simulator-using-matlab-16 

Aim: To create a Rankine Cycle simulator in MATLAB. Objectives: The code should calculate the state point variables based on user inputs. To plot the T-S diagram for the Rankine cycle. To plot the H-S diagram for the Rankine cycle. Rankine cycle: The Rankine cycle is one of the many thermodynamic cycles whose principles…

Please find the link below that leads to the project that solves the given file parsing assignment.   https://skill-lync.com/projects/demostrating-file-parsing-in-matlab-by-parsing-nasa-thermodynamic-data 

Aim: To demonstrate file parsing for the given NASA thermodynamic data . Objectives of the project: To extract the 14 coefficients and calculate the Specific Heat, Enthalpy and Entropy for each of the species in the given data file. Calculate the molecular weight of each species Plot the Specific Heat, Enthalpy, and…

Please refer to the following link to view the solution to the assignment.   https://skill-lync.com/projects/demonstrating-the-genetic-algorithm-in-matlab 

Aim: To write a code in MATLAB to optimize the stalagmite function and find the global maxima of the function. Objectives of the project: To understand the concept of the Genetic Algorithm. Write a MATLAB code to plot the stalagmite function. Use the Genetic Algorithm to maximize the stalagmite function and study three…

Aim: To write a code in MATLAB to demonstrate curve fitting. Objectives of the project: To write code to fit a linear and cubic polynomial for the given temperature vs specific heat data. To plot the linear and cubic fit curves along with the raw data points. To write a code to demonstrate splitwise curve fitting method.…

The assignment can be viewed by clicking on the project link below:https://skill-lync.com/projects/to-simulate-a-simple-pendulum-by-solving-a-second-order-ode-using-matlab 

Aim: To write a program in MATLAB that simulates the motion of a simple pendulum by solving a second-order Ordinary Differential Equation. Ordinary Differential Equations:- Ordinary Differential Equations (ODEs) are the equations that contain derivatives of a function, and we usually try to solve for the derivatives. The…

Aim: To write a MATLAB program to solve for an Ideal Otto Cycle with the following requirements, The program should create a PV diagram. The program should output the thermal efficiency of the engine. Otto cycle: An Otto cycle is one of the Air-Standard cycles that describe the workings of a typical spark-ignition internal…