A discrete geometric approach for simulating the dynamics of thin viscous threads

摘要: We present a numerical model for the dynamics of thin viscous threads based on discrete, Lagrangian formulation smooth equations. The makes use condensed set coordinates, called centerline/spin representation: kinematic constraints linking centerline@?s tangent to orientation material frame is used eliminate two out three degrees freedom associated with rotations. Based description twist inspired from discrete differential geometry and variational principles, we build full-fledged thread model, which includes in particular representation internal stress. Consistency classical, equations established formally. Our method validated against reference solutions steady coiling. it possible simulate unsteady behavior robust efficient way, including combined effects inertia, stretching, bending, twisting, large rotations surface tension.