Inaccurate enthalpy and Temperature distributions

okolekar commented 1 year ago

The enthalpy and temperature distributions show inconsistent change. I think that the temperature distribution should not just fluctuate. I mean to say that the distribution should be gradual for example 0.1 0.05 0 -0.05 -0.08 and so on indicating that the top part of the material is absorbing heat and melting and the lower portion should be receiving heat and the temperature below the 0 should not be positive indicating that the lower point is at a higher temperature than the layer above it. Below is the attached screenshot of the output. The issue is encountered at 1st time step but the Newton Raphson Scheme converged for this time step I also have a temperature vs node number chart plotted below it shows a negative slope should be positive!

okolekar commented 1 year ago

An Improvement has been recorded with many changes in the code. But the difference was made by change the delta t or time step. Also the total nodes are kept constant to 11 For time step = 0.01 We have following results The Temperature profile is as follows For time step = 0.0001 And the temperature distribution is

okolekar commented 1 year ago

The new version has following changes made, 1) Added a test to check if the addition of the shape function is unity. 2) Check added if the addition of the derivatives of the shape function at a constant open coefficient is 0. 3) Test added for the Jacobian to check if the addition of the Jacobian at the end of the gaussian loop is equal to the element length 4) Dependency of the convergence of the Newton Raphson Scheme on the number of elements is still not resolved in this version Heat Transfer Verification is as below:-

Analytical Solution:

T = 2T1cos(pix)e^(pi^2alphadelt)

The below is the graph for comparison of the analytical result with the numerical scheme with the Ta assumed to be 0 and with 11 elements convergence in 4 NRS iterations

11_4nrs