Resolve the "bioheat equation" problem using the input files described which can be found in the ENGS 105 Library, in the data section from the last assignment but add a two-level time-stepping scheme for general theta. Note that the time-derivative of temperature is multiplied by the tissue specific heat and tissue density (see the tissue property table at the end of the problem statement for the values to use for each tissue type).
Start with theta= 0.5, and experiment with the time-step size to generate an accurate transient solution. To demonstrate your solution is accurate, plot the time-history of a few nodes in the bladder and tumor regions for the two blood flow cases and show that reducing the time-step does not change the nodal histories substantially (you decide what to consider "substantial", for example, an engineering solution might be < 10%, whereas a scientific solution might be < 1%, and state your criterion).
Then, try theta < 0.5, and experiment with the stability of the system as a function of the time-step size. Include, theta = 0 in your testing. How does the actual time-step required for a stable solution compare with theory? How does the mesh play into what you observe?
Specific files available for use are: