✍ Scribed by Malik Muhammad Nazeer; Muhammad Afzal; Gul Feroze Tariq; Naseer Ahmed
No coin nor oath required. For personal study only.
In this work, global solution approach for mathematical model consisting of set of hyperbolic partial, ordinary differential and algebraic equations of unsteady flow in a complex heterogeneous pipe network have been presented. The pipe network contains buffer tanks, valves, bends, pipe junctions, dead volumes and centrifuge machines connected in multiple closed loops. The mathematical model takes into account very low pressures in the centrifuge system and various flow regimes encountered therein. The differencing of the Hyperbolic partial differential equations (PDEs) is carried out with the help of Crank-Nicklson and fully implicit methods. The computational algorithm for solving the system of resulting equations exploits the sparsity of the generated matrix. Some new techniques are developed and the existing techniques have been improved for the faster convergence and lesser computer storage requirements.
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