The article investigates the existence and uniqueness of steady-state solutions to the equations governing fluid flow in pipeline networks.
Key highlights:
For fluids with a scaled monomial equation of state, like the ideal gas, the authors prove that a unique generalized potential-solution exists for the steady-state fluid flow equations in pipeline networks.
If the generalized potential-solution has non-negative potentials, then a generalized pressure-solution also exists.
For non-ideal gases following the CNGA equation of state, the existence of a generalized pressure-solution remains an open question. However, the authors construct an alternative system that always has a unique solution, and this solution is shown to be a good approximation of the true solution.
The results are applicable to other fluid flow networks, such as water distribution or carbon dioxide transport, as long as the equation of state and resistance function satisfy certain conditions.
The existence result enables correct diagnosis of algorithmic failure, problem stiffness, and non-convergence in computational algorithms for solving the steady-state fluid flow equations.
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by Shriram Srin... at arxiv.org 04-10-2024
https://arxiv.org/pdf/2309.04494.pdfDeeper Inquiries