Model and Discretization Error Adaptivity within Stationary Gas Transport Optimization

TL;DR

This paper introduces an adaptive optimization approach for stationary gas transport that dynamically balances model complexity and discretization detail to meet error tolerances, improving cost efficiency.

Contribution

It presents a novel adaptive method that controls model and discretization errors in gas transport optimization, with proven convergence and practical numerical demonstrations.

Findings

Adaptive error control improves optimization accuracy.

The method guarantees error tolerances are met.

Numerical examples validate the approach.

Abstract

The minimization of operation costs for natural gas transport networks is studied. Based on a recently developed model hierarchy ranging from detailed models of instationary partial differential equations with temperature dependence to highly simplified algebraic equations, modeling and discretization error estimates are presented to control the overall error in an optimization method for stationary and isothermal gas flows. The error control is realized by switching to more detailed models or finer discretizations if necessary to guarantee that a prescribed model and discretization error tolerance is satisfied in the end. We prove convergence of the adaptively controlled optimization method and illustrate the new approach with numerical examples.