Week 3.5 - Deriving 4th order approximation of a 2nd order derivative using Taylor Table method

Aim: To simulate wedge flow using OPENFOAM for different angles of wedge and to capture the results that are obtained from the given angles for flow. Simulation Flow Through a Pipe in OPENFOAM: Objective: 1. The main objective of the project is to simulate the flow through the pipe in OPENFOAM software. Procedural Steps:…

Objectives: 1. To simulate a 2D incompressible flow through a cylinder pipe in OPENFOAM. 2. Compare the velocity profile and maximum shear stress for the fully developed flow along with the pressure drop with the Hagen-Poiseuille's equation. 3. To make arrangements for the saving of computational resources and time…

Simulation of a Backward-Facing Step in OPENFOAM: Aim: 1. Simulate an incompressible-laminar-viscous flow through the backward facing geometry. 2. Perform transient simulation; choose solver based on the desired physics of the flow in the problem statement. 3. Explain simulation process and way of setting up…

Finite Difference Method(FDM): This method solves the equation after dividing it into single points or nodes. This method involves solving the discretizations using the differencing equations. This method uses 3 different discretization schemes. They are: 1. Forward Differencing Scheme(FDS) 2. Backward Differencing Scheme(BDS)…

Aim: Simulating quasi 1D supersonic flow through a converging-diverging nozzle using MacCormack method. Objective: 1. Deducing the conservative and non-conservative forms of governing eqns. and implementing MacCormack method to solve the eqns. and comparing the results. 2. Comparing the steady-state distribution of fluid…

Problem Statement: To solve the 2D Heat Conduction Eqn. for steady state and unsteady state by explicit and impicit method with given boundary conditions. Using implicit method, solve using different iterative solvers i.e. Jacobi, Gauss-Seidal, SOR, etc. for both steady and transient state heat conduction eqn. The accuracy…

Aim: To derive and write a program for fourth order approximation of a second order derivative in MATLAB by the following methods: 1. Central Difference 2. Skewed Right Sided Difference 3. Skewed Left Sided Difference Objective: 1. To evaluate the second order derivative of the function `f(x)=exp(x)*cos(x)`using above…