Curvilinear

Derivation of the Perturbation Curvilinear Method

Ben R. Hodges

Abstract:

This technical report presents detailed derivations of a perturbation curvilinear approach that can be applied to numerical modeling of rivers, estuaries and reservoirs wherein the channel width is small compared to the radius of curvature of bends. The report complements the manuscript by Hodges and Imberger: “A perturbation curvilinear form of the Navier-Stokes equations,”Centre for Water Research ED1120BH (2000).

This technical report provides all the mathematical details for Hodges and Imberger (2001), published in the Journal of Hydraulic Engineering <more here>
The idea behind this work is really cool, but no one has picked it up as yet. We show that you can rewrite the full curvilinear equations for a river in a perturbation form so that the left-hand side looks like the simple Cartesian N-S equations, and the right-hand side is guaranteed to be small perturbation terms. It allows you to take a standard Cartesian N-S solver and just add some small terms to make it a curvilinear solver. This method also allows you to estimate the error made by “straightening” a river (or reservoir); i.e. neglecting the right-hand side perturbation terms.