1. Central Difference To calculate number of nodes for central differencing, order of accuracy P = Number of nodes in the stencil N - order of derivative Q + 1 we know, P = 4, Q = 2. Solving for N we get N = 5 Let `(d^2f)/dx^2 = a f(i-2) + b f(i-1) + c f(i) + df(i+1) + e f(i+2)` we have to create a taylor's…

Steady state is referred to when the temperature with respect to time does not change. Unsteady/Transient State is shen the temperature with respect to time does change. The 2nd order partial diffential equation for Unsteady State is: `(delta T)/(delta t) - alpha *((delta^2T)/(delta x^2) + (delta^2T)/(delta y^2)) = 0`…

Simulation of a 1D Super-sonic nozzle flow simulation using Macormack Method In this project, I will be solving a 3D nozzle flow simulation which has been converted to a 1D nozzle, disregarding any change in quantities in the y and z directions.     This type of flow is called quasi-one-dimensional flow. This…

In this project, I will be simulating an incompressible-laminar-viscous flow through a backward facing step. This will be solved using the software OpenFOAM running on Debian. The solver for this simulation was chosen to be icoFoam, I decided what solver to use from this guide on OpenFOAM's website This is from their guide,…