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Nonlinear Interaction of Friction and Interpolation Errors in Unsteady Flow Analyses

This paper underpins numerical integration aspects of Vardy’s software. It is easy to model accurately the behaviour of pressure waves in pipes when interpolation is unnecessary and friction is negligible, but much more challenging to do so when interpolation is unavoidable and friction is not negligible – as in extensive networks of water pipes or railway tunnels. This paper is restricted to stationary boundaries and low Mach numbers, but it provides quantitative evidence that enables informed design of numerical grids in 1-D software. It shows that the key interaction is between interpolation-errors and absolute-friction, not between interpolation-errors and friction-errors.