Problem 2 - cΒΆ

  1. Plot both temperature contours and centerline profiles (T vs. \(x\) or \(y\) through center) for each different method.

  • CASE1: Jacobi method

    1. Temperature contour
    ../../_images/prob2_NumericalJacobi.png
    1. Temperature along the center line
    ../../_images/solutions_Jacobi.png
    • Converged at 2068th iteration
    • Averaged error: 1.75249104594e-06
    • Calculation time: 27.746111 [sec]

  • CASE2: Gauss-Seidel method

    1. Temperature contour
    ../../_images/prob2_NumericalGS.png
    1. Temperature along the center line
    ../../_images/solutions_GS.png
    • Converged at 1034th iteration (faster than Jacobi method by a factor of 2)
    • Averaged error: 1.74474732047e-06
    • Calculation time: 13.999504 [sec]

  • CASE2: Successive Over-Relaxation (SOR) method (Variant form of G-S method): \(\alpha\) = 1.2

    1. Temperature contour
    ../../_images/prob2_NumericalSOR.png
    1. Temperature along the center line
    ../../_images/solutions_SOR.png
    • Converged at 689th iteration (faster than Jacobi method by a factor of 3)
    • Averaged error: 1.72946829409e-06
    • Calculation time: 9.319121 [sec]