The field of radionuclide transport has long recognised the stochastic nature of the problems
encountered. Many parameters that are used in computational models are very difficult,
if not impossible, to measure with any great degree of confidence. For example,
bedrock properties can only be measured at a few discrete points, the properties between
these points may be inferred or estimated using experiments but it is difficult to achieve
any high levels of confidence.
This is a major problem when many countries around the world are considering deep
geologic repositories as a disposal option for long-lived nuclear waste but require a high
degree of confidence that any release of radioactive material will not pose a risk to future
populations.
In this thesis we apply Polynomial Chaos methods to a model of the biosphere that is
similar to those used to assess exposure pathways for humans and associated dose rates
by many countries worldwide.
We also apply the Spectral-Stochastic Finite Element Method to the problem of contaminated
fluid flow in a porous medium. For this problem we use the Multi-Element
generalized Polynomial Chaos method to discretise the random dimensions in a manner
similar to the well known Finite Element Method. The stochastic discretisation is then
refined adaptively to mitigate the build up errors over the solution times.
It was found that these methods have the potential to provide much improved estimates
for radionuclide transport problems. However, further development is needed in order to
obtain the necessary efficiency that would be required to solve industrial problems.