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

Objective: 1. To simulate a 2D incompressible laminar flow through a cylinder pipe in OpenFOAM. 2. Compare the velocity profile and maximum shear stress for the fully developed flow along with pressure drop with the Hagen Poiseuille's Equation. 3. To make arrangements to save computational resources and time by reducing…

TO EXPLAIN THE NEED FOR THE INTERPOLATION SCHEMES AND FLUX LIMITER IN THE FVM(FINITE VOLUME METHOD). Aim: To describe the need for the interpolation schemes in the FVM and flux limiter. METHOD OF THE CFD: To solve the real-world problem, the people discovery three simples schemes for the numerical solution are Finite Difference…

Simulation of a backward-facing step in OpenFOAM Aim:- Simulate an incompressible-laminar-viscous flow through the backward facing step geometry. Perform transient simulation; choose solver based on the described physics of the flow in problem statement. Explain simulation process and way of setting up the problem statement…

Objective: To Simulate the isentropic flow through a Quasi 1D subsonic nozzle by deriving both the conservation and non-conservation forms of the governing equations and solve them by implementing the MacCormack's technique using MATLAB. Problem Statement: Determine the steady-state temperature distribution for the flow-field…

Problem Statement: To solve for 2D heat conduction equation for steady state and unsteady state by explicit and implicit method with given boundary conditions. Using implicit method Solve using different iterative solvers i.e., Jacobi, Gauss seidel and Successive over relaxation for both steady and transient state heat…

Theory and derivations: While solving a CFD problem, we come across PDE which may consists 2nd order derivative. Due to complexity of the equation we may have to choose numerical approach rather than analytical. But when dealing with numerical approach we try to make the error margin as low as possible.  As the order…