FVM Interpolation and Gradient Schemes

    Problem Statement: Derivation of Central difference, Skewed right-sided difference and Skewed left-sided difference for 4th order approximations of the second-order derivative. Also, a program in Matlab to evaluate the second-order derivative of the analytical function exp(x)*cos(x) and compare…

Topic: Simulation of flow through a pipe in OpenFoam. Theory: Source https://en.wikipedia.org/wiki/Entrance_length#/media/File:Development_of_fluid_flow_in_the_entrance_region_of_a_pipe.jpg   When the liquid enters the pipe, the viscous boundary layers grow up downstream, the axial flow slows down and the central…

Symmetry vs Wedge vs HP equation: Problem: To simulate the flow in pipe using Symmetry Boundary Conditions Theory: Symmetry Boundary Constraint This boundary condition enforces a symmetry constraint.  Usage Example of the boundary condition specification:  patch name  { type  symmetry; } The…

Finite Volume Method: The Finite Volume Method is based on the approximate solution of the integral form of the conservation equations. The problem is divided into a non-overlapping set of control volumes and conservation equations are applied to each of them. Fig-1 Interpolation Schemes: The approximations of surface…

Topic:- Blockmesh Drill down  Theory:-  The main objective of this program is to design the following the figure by creating blocks ( as I have, with 9 blocks) and then create mesh according to how to view flow.Then use the icoFOAM solver to simulate the flow through a backward facing step. To understand the…

Problem Statement: Simulation of a 1D Super-sonic nozzle flow simulation using Macormack Method. To Figure out the minimum number of cycles for which the simulation should be run in order for convergence. To Compare the normalized mass flow rate between the conservative forms and non-conservative forms and make suitable…

Steady-state analysis & Transient State Analysis Solve the 2D heat conduction equation by using the point iterative techniques by implementing the following methods 1. Jacobi 2. Gauss-seidel 3. Successive over-relaxation Unsteady Thermal Conduction: Consider a stationary fluid where heat is transferred by thermal…

Objective: Your objective is to write a program that solves the ODE that represents the equation of motion of a simple pendulum with damping. Concept: In Engineering, ODE is used to describe the transient behavior of a system. A simple example is a pendulum. The way the pendulum moves depends on the Newtons second…

Objective: To read the file 'engine_data.out' and perform the following operations on the data. 1.) Data Visualizer 2.) Compatability Check 3.) Basic Performance Calculation Concept: Basic concept is to read the file 'engine_data.out' perform several functions on it. As Sublime doesn't allow you to input the…

1. a)Popt: Popt gives the optimal values of the parameters. For ex: if the equation is ax+b, the curve_fit will return the optimal values of a & b in popt.     b)Pcov: Pcov gives the estimated covariance of popt. It is used to calculate the standard deviation errors on the parameters using np.sqrt(np.diag(pcov)).…

Objective: Write a program in python to simulate the forward kinematics of a 2R Robotic Arm Ideology: The idea behind project was to basically write to the software about two links and to show the movement of each link at different angles so that from the starting i.e. when both of them have angles at 0 degrees…

Objective: In determining the minimum cushion pressure needed to break a given thickness of iceusing an air cushion vehicle, Muller derived the equation P3(1-β2)+(0.4hβ2-σh2/r2)p2+ σ2h4p/(3r4)+( σh2/3r2)3 =0 where; β = 0.5, r = 40 feet and σ = 150 pounds per square inch (psi) …

Objective: To write code that can solve an otto cycle and make plots for it and fulfill the following requirements:  1.The code should create a PV diagram 2.The output should be the thermal efficiency of the engine. Ideology: The idea behind the project is to basically first make a program that plots and…