Conveners
Hyperbolic viscous flow using Quaternions
- Simone Chiocchetti (University of Cologne)
Description
This presentation is concerned with eliminating some difficulties that can be encountered in the evolution of partial differential equations based on matrix-valued states, like for example the inverse deformation gradient "tensor" in Eulerian hyperelasticity, sometimes called "distortion", as used in the unified model of continuum mechanics by Godunov, Peshkov, and Romenski.
In this framework, fluids are represented as visco-elasto-plastic solids with arbitrarily large deformations. We show the benefits of casting the governing equations in a new state space based on a quaternion field, motivated by the breakdown of traditional discretization schemes in under-resolved fluid simulations.
We present results employing both Cartesian and unstructured Voronoi meshes, showing that the proposed quaternion-field representation can capture extremely fine features in the distortion field even when standard second-order methods are used. This is thanks to the peculiar interaction of the quaternion PDE with Godunov-type flow solvers.
The results include numerical examples of low- and high-Reynolds number simulations in two and three dimensions, which could not be carried out with the previous formulation of the model.
