Frank-Oseen Model for Liquid Crystal Dynamics

In our research, we expand on professor Franziska Weber’s finite difference method for computing three dimensional wave maps into spheres by letting the three Frank elastic constants differ from each other. Before going further, we confirmed the physical realism of the smooth model by showing that it conserves energy. The main focus of our work is the discretization of this generalized model, and we have proved that the discrete model is indeed energy conserving. We translate our results into a simulation where we can change initial conditions, elastic constants, and boundary conditions and explore the findings.