Effect of variation of Time Steps on 1D Linear Convection Equation

Objective The objective of this project is to simulate the Hagen-Poiseuille Flow through a pipe in OpenFOAM using the symmetry boundary conditions. This project is a continuation of the previous project in which the Hagen-Poiseuille Flow was simulated using the wedge boundary conditions using a reduced model of the long…

Objective The objective of this project is to numerically simulate the Hagen Poiseuille flow through a pipe in OpenFOAM by accomplishing the following objectives.  Writing a program in MATLAB to automate the generation of the computational mesh for any wedge angle and grading schemes. Wedge angle should be less than…

Objective The objective of the project is to simulate the flow over a Backward Facing Step using OpenFOAM, and to determine the effect of mesh grading factor on the magnitude of velocity of the flow profile.  The above figure shows the geometry of the backward facing step through which the flow is to be simulated.…

Objective To write code in MATLAB to solve and simulate the Quasi 1D Supersonic Nozzle Flow Equations using the MacCormack Method, by implementing both the conservative and non-conservative forms of the governing equations. To perform grid dependence test. To determine the minimum number of runs for which the simulation…

Steady and Unsteady 2D Heat Conduction The steady state and unsteady (transient) state equations for the 2 dimensional Heat Conduction are given as,  `(delT)/(delt) = alpha ( (del^2T)/(delx^2) +(del^2T)/(dely^2))` - Transient 2D Heat Conduction  For Steady State, `(dT)/dt = 0` `(del^2T)/(delx^2) + (del^2T)/(dely^2)…

Objective The objective of the problem is to analyze the effect of time step on the stability of the solution for both implicit and explicit schemes of the 2D Transient Heat Conduction Equation. The stability of a numerical method for analysing an explicit time integration problem depends on the CFL Number or Cournat Number…

Objective  The objective of this problem is to write the MATLAB code to solve the 1D Linear Convection Equation for different values of time steps Convection Convection is basically defined as the bulk movement of a fluid from one position to another with a particular velocity. An example of convection in fluids can…

Objective The objective of the project is to write the MATLAB code to simulate the motion of a pendulum by solving the equation that represents the motion of the pendulum with damping.  The equation that describes the motion of the pendulum is given as,  `(d^2theta)/(dt^2)+(b/m)(d theta )/(dt) + (g/L)sin theta…

Objective The objective of this problem is to compare and plot the effect of grid size (dx) on the Errors in Approximations. The first order error, second order error and fourth order error were calculated in the previous problem by considering a constant grid size (dx) value. Here, we plot the relationship between dx…

Objective The aim of the project is to determine and plot the comparison and effect of number of moles of Carbon (c) on the Stoichiometric Coefficient (ar) for the Combustion Reaction.  Stoichiometric combustion offers an easy way to understand combustion concepts. When fuel and air mix they produce products  as…