A mass-conservative control volume-finite element method for solving Richards’ equation in heterogeneous porous media

We present a mass-conservative vertex-centred finite volume method for efficiently solving the mixed form of Richards’ equation in heterogeneous porous media. The spatial discretisation is particularly well-suited to heterogeneous media because it produces consistent flux approximations at quadrature points where material properties are continuous. Combined with the method of lines, the spatial discretisation gives a set of differential algebraic equations amenable to solution using higher-order implicit solvers. We investigate the solution of the mixed form using a Jacobian-free inexact Newton solver, which requires the solution of an extra variable for each node in the mesh compared to the pressure-head form. By exploiting the structure of the Jacobian for the mixed form, the size of the preconditioner is reduced to that for the pressure-head form, and there is minimal computational overhead for solving the mixed form. The proposed formulation is tested on two challenging test problems. The solutions from the new formulation offer conservation of mass at least one order of magnitude more accurate than a pressure head formulation, and the higher-order temporal integration significantly improves both the mass balance and computational efficiency of the solution.

Improved image quality for x-ray CT imaging of gel dosimeters

Purpose: This study provides a simple method for improving precision of x-ray computed tomography (CT) scans of irradiated polymer gel dosimetry. The noise affecting CT scans of irradiated gels has been an impediment to the use of clinical CT scanners for gel dosimetry studies. Method: In this study, it is shown that multiple scans of a single PAGAT gel dosimeter can be used to extrapolate a ‘zero-scan’ image which displays a similar level of precision to an image obtained by averaging multiple CT images, without the compromised dose measurement resulting from the exposure of the gel to radiation from the CT scanner. Results: When extrapolating the zero-scan image, it is shown that exponential and simple linear fits to the relationship between Hounsfield unit and scan number, for each pixel in the image, provides an accurate indication of gel density. Conclusions: It is expected that this work will be utilised in the analysis of three-dimensional gel volumes irradiated using complex radiotherapy treatments.