Error Magnitude Comparison with respect to 1D mesh size dx of 4th order approximations of the second-order derivative using Finite Difference Method

Objective:  1. To simulate a 1D Quasi subsonic-supersonic flow inside a convergent-divergent nozzle with 2nd order accuracy using MacCormack's Explicit Method. 2. To compare the numerical results obtained from both conservative form and non-conservative form with the analytical results and draw a line of superiority…

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:  1. To simulate 2D laminar incompressible flow through backwards-facing step using Finite Volume Method and to plot the velocity contour and line plot of velocity at the step. 2. To create the geometry using blockMesh utility 3. To a solver which is cable of solving a laminar and incompressible flow 4. To observe…

Objective: To find the significance of Spectral radius on the converge and stability of a linear system Theory:  The solution of a system of linear equations can be found by implementing the iterative solvers namely, Jacobi, Gauss-Seidal and SOR. However the before starting to solve a system, we can predict the…

Objective:  To solve a heat conduction equation of a 2D plate surrounded by constant temperature by Finite Difference Method. Here we will consider both the steady-state and transient cases and compare by which iterative method results with better accuracy with less number of iteration can be obtained. Also, we will…

Objective: `(delu)/(delt) + C(delu)/(delx) =0` To solve the above mentioned 1D Linear Convection Equation using Finite Difference Method where forward differencing is used for the time derivative term and backward differencing is used for the space terms. The initial velocity and the final velocity is to be compared for…

Objective: Stoichiometric combustion offers an easy way to understand combustion concepts. When fuel and air mix they produce products as CO2, CO, OH, H2O, NO, N2O and many more. In stoichiometric combustion, we make a simple assumption that the by-products are only CO2, H2O and N2. For a generic alkane fuel, the combustion…

Objective:  The main target is to find the 4th order approximations of the 2nd order derivative of the function f(x) = exp(x)*cos(x) using all the 3 numerical approximations methods namely, Central Difference Method, Skewed Right-Sided Difference Method and Skewed Left-Sided Difference Method. Then we need to compute…

Objective:  In Engineering, ODE is used to describe the transient behaviour of a system.  A simple example is a pendulum   The way the pendulum moves depends on the Newtons second law. When this law is written down, we get a second order Ordinary Differential Equation that describes the position of the "ball"…