Travelling Wave Solutions on a Cylindrical Geometry

Fluid equations are generally quite difficult and computationally-expensive to solve. However, if one is primarily interested in how the surface of the fluid deforms, we can re-formulate the governing equations purely in terms of free surface variables. Reformulating equations in such a way drastically cuts down on computational cost, and may be useful in areas such as modelling blood flow. Here, we study one such free-boundary formulation on a cylindrical geometry

Modelling Travelling Waves on Elastic Blood Vessels

Traditional methods for modelling blood flow are often prohibitively computationally expensive, particularly in the case of blood vessels with elastic walls. This is because such methods rely on computing a mesh based on the vessel geometry and then recomputing the mesh when the geometry changes. We plan to change this approach by adapting methodology available from analysing free boundary problems where coordinate transformations are used to setup the problem in terms of the moving boundary instead. The work thus far focuses on; studying free boundary formulations, particularily for travelling waves on a cylindrical geometry, found in the literature; alongside studying/assessing software packages already available for blood flow modelling