Inverse Problem of Pipeline Transport of Weakly-Compressible Fluids

Nonstationary one-dimensional flow of a weakly-compressible fluid in a pipeline is considered. The flow is described by a nonlinear system of two partial differential equations for the fluid flow rate and pressure in the pipeline. An inverse problem on determination of the fluid pressure and flow rate at the beginning of the pipeline needed for the passage of the assigned quantity of fluid in the pipeline at a certain pressure at the pipeline end was posed and solved. To solve the above problem, a method of nonlocal perturbation of boundary conditions has been developed, according to which the initial problem is split at each discrete moment into two successively solvable problems: a boundary-value inverse problem for a differential-difference equation of second order for the fluid flow rate and a direct differential-difference problem for pressure. A computational algorithm was suggested for solving a system of difference equations, and a formula was obtained for approximate determination of the fluid flow rate at the beginning of the pipeline. Based on this algorithm, numerical experiments for model problems were carried out.