2 citations · 2 across the 8 of their papers we have counts for
9 papers
A Finite Element Method for the Grad--Mercier Equation
Ben Ashby, Tristan Pryer
We develop and analyse a conforming piecewise affine finite element method for the Grad--Mercier equation, a nonlocal elliptic model for magnetic equilibria whose source depends on…
Characteristic Sweeps and Source Iteration for Charged-Particle Transport with Continuous Slowing-Down and Angular Scattering
Ben S. Ashby, Alex Lukyanov, Tristan Pryer
We develop a semi-analytic deterministic framework for charged-particle transport with continuous slowing-down in energy and angular scattering. Directed transport and energy advec…
A finite element method for a non-Newtonian dilute polymer fluid
Ben S. Ashby, Gabriel R. Barrenechea, Alex Lukyanov +2
We study the discretisation of a uniaxial (rank-one) reduction of the Oldroyd-B model for dilute polymer solutions, in which the conformation tensor is represented as $\sig = \vec…
Modelling and Analysis of Non-Contacting Mechanical Face Seals with Axial Disturbances and Misalignment
Ben S Ashby, Tristan Pryer, Nicola Y Bailey
Advancements in industrial applications are driving developments in non-contacting mechanical seal technology. Key requirements include improvements in efficiency and reliability,…
A Positivity-Preserving Finite Element Framework for Accurate Dose Computation in Proton Therapy
Ben S. Ashby, Abdalaziz Hamdan, Tristan Pryer
We present a stabilised finite element method for modelling proton transport in tissue, incorporating both inelastic energy loss and elastic angular scattering. A key innovation is…
A nodally bound-preserving finite element method for hyperbolic convection-reaction problems
Ben S. Ashby, Abdalaziz Hamdan, Tristan Pryer
In this article, we present a numerical approach to ensure the preservation of physical bounds on the solutions to linear and nonlinear hyperbolic convection-reaction problems at t…
Efficient Proton Transport Modelling for Proton Beam Therapy and Biological Quantification
Ben S. Ashby, Veronika Chronholm, Daniel K. Hajnal +4
In this work, we present a fundamental mathematical model for proton transport, tailored to capture the key physical processes underpinning Proton Beam Therapy (PBT). The model pro…
Duality based error control for the Signorini problem
Ben S. Ashby, Tristan Pryer
In this paper we study the a posteriori bounds for a conforming piecewise linear finite element approximation of the Signorini problem. We prove new rigorous a posteriori estimates…
Discretisation of an Oldroyd-B viscoelastic fluid flow using a Lie derivative formulation
Ben S. Ashby, Tristan Pryer
In this article we present a numerical method for the Stokes flow of an Oldroyd-B fluid. The viscoelastic stress evolves according to a constitutive law formulated in terms of the…