Deraviation of 4th order approximations of the second-order derivative using various schemes:- The given function is  `exp(x)*cos(x)` The second derivative is :- `-2*exp(x)*sin(x)` 1. Central Difference Scheme:- As given, no. of Nodes (N) required for 4rth order approximation (P = 4) of 2nd order deravative (Q…

The governing equation for 2-D heat conduction is : 2-D Transient :- `{delT}/{delt} + alpha ({del^2T}/{delx^2}+{del^2T}/{dely^2}) = 0` where `alpha` is the thermal diffusivity of the medium.       Descritizing the above equation we get:- `{T_(i,j)^(n+1) - T_(i,j)^(n)}/{Deltat} + alpha*({{T_(i-1,j) -2*T_(i,j)…

Simulation of a 1D Super-sonic nozzle flow simulation using Macormack Method Schematic representation of convergent divergent nozzle. In the above described convergent divergent nozzle, while simulating for the flow parameters, an assumptions has been made that the flow property will only vary with x. Thus the uniform…

Simulation of a backward facing step in OpenFOAM  The project demonstrates importance of grading factor while meshing in CFD numerical simulation. Geometry for analysis:- In order to develop this geometry to be solved in openFoam, 3 blocks were made and meshed using blockMesh. The blocks created is described below:-…