arXiv subjects

Mike Cullen

Publications and source records attributed to Mike Cullen.

4 recordsLinked to original sources

arXiv2016

Convection in a Single Column -- Modelling, Algorithm and Analysis

The group focused on a model problem of idealised moist air convection in a single column of atmosphere. Height, temperature and moisture variables were chosen to simplify the mathematical representation (along the lines of the Boussinesq approximation in a height variable defined in terms of pressure). This allowed exact simple solutions of the numerical and partial differential equation problems to be found. By examining these, we identify column behaviour, stability issues and explore the feasibility of a more general solution process.

physics.ao-ph↗

arXiv2016

Recent progress and review of issues related to Physics Dynamics Coupling in geophysical models

Geophysical models of the atmosphere and ocean invariably involve parameterizations. These represent two distinct areas: Subgrid processes that the model cannot resolve, and diabatic sources in the equations, due to radiation for example. Hence, coupling between these physics parameterizations and the resolved fluid dynamics and also between the dynamics of the air and water, is necessary. In this paper weather and climate models are used to illustrate the problems. Nevertheless the same applies to other geophysical models. This coupling is an important aspect of geophysical models. However, often model development is strictly segregated into either physics or dynamics. As a consequence, this area has many unanswered questions. Recent developments in the design of dynamical cores, extended process physics and predicted future changes of the computational infrastructure are increasing complexity. This paper reviews the state-of-the-art of the physics-dynamics coupling in geophysical models, surveys the analysis techniques, and illustrates open questions in this field. This paper focuses on two objectives: To illustrate the phenomenology of the coupling problem with references to examples in the literature and to show how the problem can be analysed. Proposals are made on how to advance the understanding and upcoming challenges with emerging modeling strategies. This paper is of interest to model developers who aim to improve the models and have to make choices on and test new implementations, to users who have to understand choices presented to them and finally users of outputs, who have to distinguish physical features from numerical problems in the model data.

physics.ao-ph↗

arXiv2015

Mesh Adaptation on the Sphere using Optimal Transport and the Numerical Solution of a Monge-Amp\`ere type Equation

An equation of Monge-Amp\`ere type has, for the first time, been solved numerically on the surface of the sphere in order to generate optimally transported (OT) meshes, equidistributed with respect to a monitor function. Optimal transport generates meshes that keep the same connectivity as the original mesh, making them suitable for r-adaptive simulations, in which the equations of motion can be solved in a moving frame of reference in order to avoid mapping the solution between old and new meshes and to avoid load balancing problems on parallel computers. The semi-implicit solution of the Monge-Amp\`ere type equation involves a new linearisation of the Hessian term, and exponential maps are used to map from old to new meshes on the sphere. The determinant of the Hessian is evaluated as the change in volume between old and new mesh cells, rather than using numerical approximations to the gradients. OT meshes are generated to compare with centroidal Voronoi tesselations on the sphere and are found to have advantages and disadvantages; OT equidistribution is more accurate, the number of iterations to convergence is independent of the mesh size, face skewness is reduced and the connectivity does not change. However anisotropy is higher and the OT meshes are non-orthogonal. It is shown that optimal transport on the sphere leads to meshes that do not tangle. However, tangling can be introduced by numerical errors in calculating the gradient of the mesh potential. Methods for alleviating this problem are explored. Finally, OT meshes are generated using observed precipitation as a monitor function, in order to demonstrate the potential power of the technique.

math.NA↗

arXiv2014

On a model of forced axisymmetric flows

In this work, we consider a model of forced axisymmetric flows which is derived from the inviscid Boussinesq equations. What makes these equations unusual is the boundary conditions they are expected to satisfy and the fact that the boundary is part of the unknown. We show that these flows give rise to an unusual Monge-Ampere equations for which we prove the existence and the uniqueness of a variational solution. We take advantage of these Monge-Ampere equations and construct a solution to the model.

math.AP↗