Numerical solution of equations describing the action of electric field on a liquid crystal

Dynamic processes in liquid crystals are investigated with the help of simplified mathematical model, describing mechanical, temperature and electrostatic perturbations. On the basis of these equations, the separate subsystem for angular velocity and tangential stress is deduced and analyzed. The problem of perturbing an extended liquid crystal layer by an electric field is considered. It is created by charges on the capacitor plates, periodically located along the layer. The right-hand sides of the second-order equations include bulk forces and moment of forces caused by the electric field action. An algorithm for numerical solution of the subsystem of equations is developed. At the first stage of this algorithm the bulk forces and moment of forces are calculated based on the equations of electrodynamics using the method of straight lines, and at the second stage the distributions of tangential stress, angular velocity and angle of rotation of the liquid crystal molecules are found using the finite-difference scheme “cross”. The algorithm is implemented as a parallel program written in C++ using CUDA technology for computing systems with graphics accelerators.