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How can I find information about the theory behind the numerical solvers used by the Bentley OpenFlows water products?
Generally speaking the theory of the how the software works is documented in the Help file included with the software, accessible from the File > Help menu (or Help > Help for older versions). In most cases you will find a Theory section on the contents tab, or you can search for "theory".
WaterCAD and WaterGEMS use a modified version of the standard EPANET solver, which solves for the distributions of flows and hydraulic grades using the Gradient Algorithm. Note that there are some enhancements added on top of the standard EPANET solver as documented here: Engine Compatibility Mode and related Calculation options
To solve the system of non-linear equations, the Newton-Raphson iterative scheme is used. You can find more information in the Help topic entitled "The Gradient Algorithm", and the topcs within the same parent article, "Pressure Network Hydraulics". For additional reference, see Appendix D of the EPANET manual, which you can download from epa.gov here.