41 citations · 62 across the 9 of their papers we have counts for
10 papers
AdHImEx: Adaptively High-Order Implicit-Explicit Transport for Large Time Steps
Amber J. te Winkel, Hilary Weller, Christian Kühnlein +1
Adaptively Implicit-Explicit (AdImEx) time stepping provides stability for large time steps for mass-conservative transport, making it attractive for the numerical representation o…
Adaptively Implicit Advection for Atmospheric Flows
Hilary Weller, Christian Kuehnlein, Piotr K. Smolarkiewicz
Implicit time-stepping for advection is applied locally in space and time where Courant numbers are large, but standard explicit time-stepping is used for the remaining solution wh…
New limiter regions for multidimensional flows
James Woodfield, Hilary Weller, Colin J Cotter
Accurate transport algorithms are crucial for computational fluid dynamics and more accurate and efficient schemes are always in development. One dimensional limiting is commonly e…
Conservation with moving meshes over orography
Hiroe Yamazaki, Hilary Weller, Colin J. Cotter +1
Adaptive meshes have the potential to improve the accuracy and efficiency of atmospheric modelling by increasing resolution where it is most needed. Mesh re-distribution, or r-adap…
Two-fluid single-column modelling of Rayleigh-Bénard convection as a step towards multi-fluid modelling of atmospheric convection
Daniel Shipley, Hilary Weller, Peter Clark +1
Multi-fluid models have recently been proposed as an approach to improving the representation of convection in weather and climate models. This is an attractive framework as it is…
Numerical methods for entrainment and detrainment in the multi-fluid Euler equations for convection
William A McIntyre, Hilary Weller, Christopher E Holloway
Convection schemes are a large source of error in global weather and climate models, and modern resolutions are often too fine to parameterise convection but are still too coarse t…
Multidimensional method-of-lines transport for atmospheric flows over steep terrain using arbitrary meshes
James Shaw, Hilary Weller, John Methven +1
Including terrain in atmospheric models gives rise to mesh distortions near the lower boundary that can degrade accuracy and challenge the stability of transport schemes. Multidime…
Dimension Splitting and a Long Time-Step Multi-Dimensional Scheme for Atmospheric Transport
Yumeng Chen, Hilary Weller, Stephen Pring +1
Dimensionally split advection schemes are attractive for atmospheric modelling due to their efficiency and accuracy in each spatial dimension. Accurate long time-steps can be achie…
Nonlinear solution techniques for solving a Monge-Ampère equation for redistribution of a mesh
P. A. Browne, J. Prettyman, H. Weller +2
A Monge-Ampère (MA) equation arises when seeking an optimally transported mesh that equidistributes a given monitor function in Cartesian space. This MA equation is a fully nonline…
Mesh Adaptation on the Sphere using Optimal Transport and the Numerical Solution of a Monge-Ampère type Equation
Hilary Weller, Philip Browne, Chris Budd +1
An equation of Monge-Ampère type has, for the first time, been solved numerically on the surface of the sphere in order to generate optimally transported (OT) meshes, equidistribut…