Asymptotic analysis of flow in wavy tubes and simulation of the extrusion process

The paper is devoted to the mathematical modelling of an extrusion process. Usually, an extruder has a very complicated geometry. This generates a lot of difficulties for computations of three-dimensional flows. In the present paper, we develop and justify the asymptotic domain decomposition strategy in order to parallelize the computational process and reduce the memory. The error estimates are proved for the Stokes steady-state equation in the two-dimensional and three-dimensional cases. Then, the asymptotic domain decomposition procedure is applied for numerical testing and computations of the non-Newtonian fluid simulating a real process of the polymer extrusion.