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

OBJECTIVE. To simulate an axis-symmetric laminar flow through the constant cross-sectional of the pipe by applying the symmetry boundary condition. To simulating for the mentioned angles i.e for 10, 25, 45 degrees using both symmetry and wedge boundary conditions and validate them with HP equations.   Hagen-Poiseuille's…

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…

OBJECTIVE. To simulate an incompressible-laminar-viscous flow through the backwards-facing step geometry and perform a transient simulation. Case 1 - To Simulate the flow without using any grading factor (i.e., GF = 1) Case 2 -  To Simulate the flow with a grading factor of 0.2. The cells should be finer…

Finite volume Method: The finite volume method (FVM) is a method for representing and evaluating partial differential equations in the form of algebraic equations. Similar to the finite difference method (FDM) or finite element method (FEM), values are calculated at discrete places on a meshed geometry. One important feature…

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…

Introduction: Explicit Method: When a direct computation is made for an unknown quatity in terms of known quantity. This computation is called Explicit. This method requires stability criteria which when statisfied leads to stable solution. Because of the stability criteria small time steps has to be taken to obtain stable…

AIM: To derive the fourth order approximations of a second order derivative using central differencing scheme, skewed right sided difference and skewed left sided difference with the help of taylor table method and to compare the analytical derivative with obtained values for the given function. SCHEME DERIVATIONS: CENTRAL…