The website of James Shaw, a PhD student researching numerical methods for the atmosphere at University of Reading

Creating a high-order finite volume transport scheme

20 January 2017

Over the last year of my PhD I have been working to create a finite volume transport scheme, called ‘cubicFit’, that is second-order convergent on arbitrary meshes. Recently, I have tried modifying the cubicFit transport scheme to obtain high-order convergence: that is, convergence greater than second-order. Here I'll introduce a one-dimensional version of the cubicFit scheme and explain how it can be modified to obtain high-order convergence.

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Advection over steep slopes

3 October 2016

There are many ways to represent terrain in atmospheric models. Terrain following coordinates are in widespread operational use but can suffer from numerical errors near steep slopes. Advection errors, and errors calculating pressure gradients both reduce model accuracy. The cut cell method is often put forward as an alternative which can reduce pressure gradient errors, but the technique may still suffer from advection errors where flow is misaligned with the mesh. Without special treatment, the cut cell method can create very small cells which constrain the timestep when explicit methods are used.

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Interactive polynomial fit visualisation

3 May 2016

This demonstration shows quadratic and cubic polynomials fitted through a set of points using a least squares approach. This technique generalises to higher dimensions and can be used as an interpolation function for solving the flux form advection equation on arbitrary meshes.

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OpenFOAM on Ubuntu 16.04

27 April 2016

If you want to use the OpenFOAM 3 on Ubuntu 16.04 Xenial Xerus, there is no binary package in the OpenFOAM repository at the time of writing.

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Beyond Stack Overflow

4 April 2016

Most researchers I know in my department make regular use of Stack Overflow, the question and answer site for programmers. While it is the oldest and most popular, there are a family of Q&A sites that closely follow the look and feel of Stack Overflow. More than a dozen of these target scientific and mathematical topics, and some are particularly relevant to those of us working in meteorology:

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