In December 2012 Christian Jacobs published the following paper in the Geophysical Journal International 2012:
Multiphase flow modelling of volcanic ash particle settling in water using adaptive unstructured meshes
C. T. Jacobs; G. S. Collins; M. D. Piggott; S. C. Kramer; C. R. G. Wilson
doi: 10.1093/gji/ggs059

Supervisor: Dr Gareth Collins

Student: Christian Jacobs

This project will develop advanced numerical methods for the simulation of multi-scale highly dynamic flows in complex domains.  A multiple phase flow model will be developed and used in a variety of shock physics applications, from impact cratering to volcanic eruptions.

Many high energy shock events, such as planetary scale meteorite impacts, are not reproducible in the laboratory and numerical models provide an important insight into their underlying physics.  Most existing models are based on finite difference techniques; describing the dynamics of a continuous medium discretised over a chessboard-like lattice of grid points in space and time.  However, such structured grids suffer from a correlation between computer storage, simulation time and the dimensionality of the problem.  This means that the cost of improving the accuracy of the solution by increasing the resolution can often make simulations untenable with available computer power.

These limitations can be overcome by using an unstructured adaptive mesh; increasing the resolution in areas of dynamic significance and decreasing it in others.  Hence solutions can be captured more accurately while maintaining computational efficiency.  This makes large-scale problems, such as atmospheric blast waves or oceanic tsumamis, tractable in complex three-dimensional domains.  Unstructured meshes offer the additional advantage of being able to accurately represent highly anisotropic structures such as material interfaces.  This allows regions with different properties to be modelled while maintaining a sharp interface between them.

In an ongoing ISP PDRA project we are developing a multimaterial modelling approach for use with unstructured adaptive meshes.  This approach is suitable for a broad range of problems where the materials involved do not interpenetrate.  Indeed, the method is efficient and accurate so long as sufficient resolution is maintained around the interface to resolve the smallest droplets or particles of interest.  However, for applications involving materials that interpenetrate on a scale finer than that resolvable by the mesh (such as particle suspensions in a fluid) a different, multiphase approach is required.  In this case, the movement of one material through another must be parameterized.

The aim of this PhD project is to extend the unstructured, adaptive multimaterial model being developed as part of the postdoctoral research modelling project into the multiphase realm.  Moreover, to maximise model flexibility and breadth of application the PhD project will explore methods to transition from a multimaterial method to a multiphase approach, where mixtures of different phases can be physically represented.  Important multi-phase applications that will be the ultimate target of the PhD project include the development and evolution of the plume of hot gas, dust and melt particles in a planetary-scale impact, and the collapse of volcanic plumes as pyroclastic flows.  Moreover, the development of multi-phase capability will enable the future investigation of the response of mixtures to extreme conditions and shocks.