Week 5 - Mid term project -Steady state vs unsteady analysis
STEADY STATE SOLUTIONS:
- The steady state solution does not involve time marching .
- Temperature Gradient does not change with respect to time .
- The number of grid points are same i.e nx=ny
Following are the results for steady state solution:
jacobi method
Number of iterations done are 217
Time taken for solving equation is 171.586736
Gauss Seidel Method:
Number of iterations done are 117
Time taken for solving equation is 0.005830
Successive Over Relaxation Method
Relaxation factor considered is 1.729454e+00
Number of iterations done are 731
OBSERVATION:
The convergence is faster in terms of time and iteration in the case of Successive Over Relaxation method than Gauss seidel and Jacobi Method.
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UNSTEADY STATE EQUATION:
- The unsteady state solution involves time marching .
- Temperature Gradient changes with respect to time .
- The number of grid points are same i.e nx=ny
- Temperature changes with respect to time reaching steady state.
Following are the results for Transient/unsteady state solution Explicity and Implicitly
1.Explicit Method
2D Unsteady Transient Heat conduction by Explicit Method
gauss sediel Unsteady Implicit
Number of iterations done are 416
Time taken for solving equation is 0.041
Successive Over Relaxation Unsteady Implicit
Relaxation Factor 1.729454
Number of iterations done are 1808
Time taken for solving equation is 0.047837
BSERVATIONS:
- Solving Implicitly involves larger number of iteration than explicit .
- Successive Over Relaxation method yields faster and takes less iteration as compared to Gauss Seidel and Jacobi method.
- Explicit method gives results faster than Successive Over Relaxation Implicit method.