2017 , Volume 22, Special issue, p.87-98

One of the approaches to mathematical modeling for deformation of a liquid crystal is based on the assumption that a liquid crystal is a fine-dispersed continuum, at each point of which the elongated particles - molecules or domains of co-oriented molecules - can move according to laws of the viscous fluid dynamics and can rotate relative to a fluid. In this approach the Cosserat continuum theory is applicable, where along with translational motion, characterized by the velocity vector, the rotational degrees of freedom for particles with the angular velocity vector are considered and, along with the stress tensor with nonsymmetrical components, the nonsymmetrical tensor of couple stresses is introduced. Within the framework of acoustic approximation of the model, which describes thermomechanical behavior of a liquid crystal taking into account the couple stresses, the system of two differential equations of the second-order was obtained for the tangential stress and angular velocity in two-dimensional case.

The algorithm for numerical solution of the obtained system of equations under given initial data and boundary conditions is considered. This system is solved using the explicit finite-difference scheme “cross” of the second-order approximation. The stability condition for the scheme is obtained. The algorithm is realized as a parallel program in the C language using the CUDA technology for computing systems with graphics accelerators. A series of computations of acoustic waves in a liquid crystal was performed to demonstrate the efficiency of proposed program. The comparison of numerical solution and the exact solution was carried out.