arXiv subjects

David Kay

Publications and source records attributed to David Kay.

4 recordsLinked to original sources

arXiv2020

Preconditioning nonlocal multi-phase flow

We propose an efficient solver for saddle point problems arising from finite element approximations of nonlocal multi-phase Allen--Cahn variational inequalities. The solver is seen to behave mesh independently and to have only a very mild dependence on the number of phase field variables. In addition we prove convergence, in three GMRES iterations, of the approximation of the two phase problem, regardless of mesh size or interfacial width. Numerical results are presented that illustrate the competitiveness of this approach.

math.NA↗

arXiv2017

Step evolution in two-dimensional diblock copolymer films

The formation and dynamics of free-surface structures, such as steps or terraces and their interplay with the phase separation in the bulk are key features of diblock copolymer films. We present a phase-field model with an obstacle potential which follows naturally from derivations of the Ohta-Kawasaki energy functional via self-consistent field theory. The free surface of the film is incorporated into the phase-field model by including a third phase for the void. The resulting model and its sharp interface limit are shown to capture the energetics of films with steps in two dimensions. For this model, we then develop a numerical approach that is capable of resolving the long-time complex free-surface structures that arise in diblock copolymer films.

physics.comp-ph↗

arXiv2014

A poroelastic model coupled to a fluid network with applications in lung modelling

Here we develop a lung ventilation model, based a continuum poroelastic representation of lung parenchyma and a 0D airway tree flow model. For the poroelastic approximation we design and implement a lowest order stabilised finite element method. This component is strongly coupled to the 0D airway tree model. The framework is applied to a realistic lung anatomical model derived from computed tomography data and an artificially generated airway tree to model the conducting airway region. Numerical simulations produce physiologically realistic solutions, and demonstrate the effect of airway constriction and reduced tissue elasticity on ventilation, tissue stress and alveolar pressure distribution. The key advantage of the model is the ability to provide insight into the mutual dependence between ventilation and deformation. This is essential when studying lung diseases, such as chronic obstructive pulmonary disease and pulmonary fibrosis. Thus the model can be used to form a better understanding of integrated lung mechanics in both the healthy and diseased states.

physics.comp-ph↗

arXiv2013

Stabilized lowest order finite element approximation for linear three-field poroelasticity

A stabilized conforming mixed finite element method for the three-field (displacement, fluid flux and pressure) poroelasticity problem is developed and analyzed. We use the lowest possible approximation order, namely piecewise constant approximation for the pressure and piecewise linear continuous elements for the displacements and fluid flux. By applying a local pressure jump stabilization term to the mass conservation equation we ensure stability and avoid pressure oscillations. Importantly, the discretization leads to a symmetric linear system. For the fully discretized problem we prove existence and uniqueness, an energy estimate and an optimal a-priori error estimate, including an error estimate for the divergence of the fluid flux. Numerical experiments in 2D and 3D illustrate the convergence of the method, show the effectiveness of the method to overcome spurious pressure oscillations, and evaluate the added mass effect of the stabilization term.

math.NA↗