Моделирование течения слабо сжимаемой жидкости при условии проскальзывания на стенке трубопровода

Abstract

The process of unsteady flow of a weakly compressible fluid through a pipeline described by a one-dimensional model in the form of a nonlinear system of partial differential equations is considered. It is assumed that the pipeline wall meets the slip condition according to Navier’s law. Within the framework of this model, the inverse problemof determining the flow velocity on the pipeline wall is posed. After discretization of the model in time, the initial problem for each discrete value of the time variable is split into two sequentially solved problems. In the first problem, a spatial variable is discretized and a special representation using the local regularization method is proposedto solve the resulting system of difference equations. As a result, an explicit formula for determining the flow velocity on the pipeline wall is obtained. After determining the distribution of the fluid flow velocity along the lengthof the pipeline, the pressure distribution is determined from the solution of the second problem.