S.D. Vynnychuk
Èlektron. model. 2024, 46(5):19-34
https://doi.org/10.15407/emodel.46.05.019
ABSTRACT
Based on the analysis of the process of solving the problem of flow distribution calculation in compressible fluid systems, which boils down to finding the root of a nonlinear system of equations using the Newton — Raphson method, methods of reducing the complexity of calculations at the stages of the iterative process are proposed. The studies belong to the class of hydraulic systems for which the total pressure change on the branch elements is a monotonic smooth function of the flow rate G. For the iterations of the Newton-Raphson method, the stages are analyzed: linearization of the nonlinear system of equations, determination of the discrepancy and error estimation, determination of cost growth and obtaining a new iterative cost value. A method and algorithm for determining the discrepancy and estimating the error with linear complexity relative to the number of branches of graph E is proposed. A method of reducing the number of unknowns in the system of flow distribution equations at the stage of forming a system of linear equations based on the use of the nodal convolution method is described. A number of variants of heuristic algorithms for determining the parameter that takes into account the rate of increase in costs when forming a new iterative value of costs and their analysis are presented.
KEYWORDS
hydraulic network, system of flow distribution equations, initial approximation, Newton — Raphson method.
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