Abstract
The lattice Boltzmann method for solid-fluid two-phase flows with a viscoelastic membrane is improved. In the present model, the elastic force at each lattice node is determined so that the total elastic energy in the whole membrane can be minimized according to the principle of virtual work. The method is applied to the motion of an annular membrane in a shear flow. The calculated deformation of the membrane agrees well with the result by the immersed boundary-lattice Boltzmann method. Next, three-dimensional structural membrane models, spherical and ellipsoidal models, are constructed by means of the mapping system. The motions of these membranes in shear flows are simulated by using the method. In an initially spherical membrane, the steady circulatory flows inside the membrane and the tank-treading motion are observed. In an initially ellipsoidal membrane, the steady shape and orientation of the membrane are almost the same regardless of initial inclination angles.
