Mid term project - Steady State vs Unsteady State Analysis

This mid-term project was done as a part of the course- Introduction to CFD using MATLAB and OpenFOAM

Steady State vs Unsteady State comparison:

• The plots obtained from the previous challenge are compared below.
• The time taken by MATLAB to complete the simulation was calculated using the tic-toc function. This time also includes the pause time of 0.03s between each iteration.
• Note: For Steady State, dt=0.0001s and for Unsteady State, dt=0.01s. Large dt was taken for unsteady state to obtain considerable changes in the plots for understanding purpose.

Steady State Successive Over-relaxation Method

Unsteady State Explicit Method

Comparison of Plots:

• For steady state simulation, the Successive over-relaxation method was the fastest with just 41 iterations and a MATLAB time of around 6s (This was calculated with the tic-toc function and includes the 0.03s pause between each iteration).
• For the unsteady state simulation, the explicit method was the fastest as compared to the implicit scheme for the same number of time steps(801). The MATLAB computation time was 116s
• For the unsteady state implicit method, the MATLAB computation time was around 140s, which is higher than the explicit method. One reason for this is the higher computation time required to solve the matrix A to get the equations in x(n) and again implementing the back-substitution process to get the values of x(n) to get temperature values. The plot is as shown below.

Note:

• The transient state simulations have to account for the temperature diffusion in the grid w.r.t time. Hence, these calculations take longer time and better results are obtained with large number of iterations.

MATLAB Computation time for different methods (s)
Steady State			Unsteady State
Jacobi	Gauss-Seidal	SOR	Explicit	Implicit
35	18	6	116	140