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Lew Rossman
2019-10-07 14:27:47 -04:00
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@@ -94,7 +94,7 @@ EPANET's original node re-ordering scheme has been replaced by the more efficien
EPANET's hydraulic solver can generate an ill-conditioned solution matrix when pipe flows approach zero unless some adjustment is made (i.e., as a pipe's flow approaches 0 its head loss gradient also approaches 0 causing its reciprocal, which is used to form the solution matrix's coefficients, to approach infinity). EPANET 2.0 used an arbitrary cutoff on head loss gradient to prevent it from becoming 0. This approach doesn't allow a pipe to follow any head loss v. flow relation in the region below the cutoff and can produce incorrect solutions for some networks (see [Estrada et al., 2009](https://ascelibrary.org/doi/full/10.1061/%28ASCE%29IR.1943-4774.0000100)). EPANET's hydraulic solver can generate an ill-conditioned solution matrix when pipe flows approach zero unless some adjustment is made (i.e., as a pipe's flow approaches 0 its head loss gradient also approaches 0 causing its reciprocal, which is used to form the solution matrix's coefficients, to approach infinity). EPANET 2.0 used an arbitrary cutoff on head loss gradient to prevent it from becoming 0. This approach doesn't allow a pipe to follow any head loss v. flow relation in the region below the cutoff and can produce incorrect solutions for some networks (see [Estrada et al., 2009](https://ascelibrary.org/doi/full/10.1061/%28ASCE%29IR.1943-4774.0000100)).
The hydraulic solver has been modified to use a linear head loss v. flow relation for flows approaching zero. For the Darcy-Weisbach equation, the linear Hagen-Poiseuille formula is used for laminar flow where the Reynolds Number is <= 2000. For the Hazen-Williams and Chezy-Manning equations, a flow limit is established for each pipe, equal to the flow that produces the EPANET 2 gradient cutoff. For flows below this a linear head loss relation is used whose gradient always equals the cutoff. EPANET 2.2 is now able to correctly solve the examples presented in Estrada et al. (2009) as well as those in [Gorev et al., (2013)](https://ascelibrary.org/doi/10.1061/%28ASCE%29HY.1943-7900.0000694) and [Elhay and Simpson (2011)](https://ascelibrary.org/doi/10.1061/%28ASCE%29HY.1943-7900.0000411). The hydraulic solver has been modified to use a linear head loss v. flow relation for flows approaching zero. For the Darcy-Weisbach equation, the linear Hagen-Poiseuille formula is used for laminar flow where the Reynolds Number is <= 2000. For the Hazen-Williams and Chezy-Manning equations, if the head loss gradient at a given flow is below the EPANET 2.0 gradient cutoff then a linear head loss relation is used whose slope equals the cutoff. EPANET 2.2 is now able to correctly solve the examples presented in Estrada et al. (2009) as well as those in [Gorev et al., (2013)](https://ascelibrary.org/doi/10.1061/%28ASCE%29HY.1943-7900.0000694) and [Elhay and Simpson (2011)](https://ascelibrary.org/doi/10.1061/%28ASCE%29HY.1943-7900.0000411).
## Pressure Dependent Demands ## Pressure Dependent Demands