[Текст] : научное издание / Ирина Владимировна Смолехо, Оксана Викторовна Садовская, Владимир Михайлович Садовский // Вычислительные технологии. - 2017. -
Т. 22,
№ S1. - С. 87-98
. - ISSN 1560-7534
Перевод заглавия: Numerical modeling of acoustic waves in a liquid crystal using CUDA technology
Аннотация: В рамках акустического приближения математической модели, описывающей термомеханическое поведение жидкого
кристалла с учетом моментных свойств, получена система уравнений второго порядка для касательного напряжения и угловой скорости. Разработан алгоритм численного решения этой системы при заданных начальных данных и граничных условиях, который реализован в виде параллельной программы на языке Си с использованием технологии CUDA для вычислительных систем с графическими ускорителями.
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.
РИНЦ Держатели документа: Институт вычислительного моделирования СО РАН
Доп.точки доступа: Смолехо, Ирина Владимировна; Smolekho Irina Vladimirovna; Садовская, Оксана Викторовна; Sadovskaya Oxana Viktorovna; Садовский, Владимир Михайлович; Sadovskii Vladimir Mikhailovich
