Avoiding singularities in the numerical solution of the motion of a deformable ellipse immersed in a viscous fluid

Geological materials are largely heterogeneous and are typically comprised of approximately ellipsoidal objects immersed in a matrix with different physical properties. Methodologies for the identification of ancient regional tectonic patterns may be developed based on an understanding of the behaviour of heterogeneous materials. In this contribution, the differential equation governing the rotation of a deformable ellipse immersed in a viscous fluid is considered and is found to contain a singularity when the ellipse becomes circular in shape. This problem is avoided by reformulating the equations using the standard algebraic representation of an ellipse. Thus, the equations can be numerically solved without difficulty.