# Adaptive Refinement Strategies for the Simulation of Gas Flow in Networks using a Model Hierarchy

## TL;DR

This paper introduces novel adaptive refinement strategies for gas flow simulation in pipeline networks, combining spatial, temporal, and model adaptivity to improve accuracy and reduce computational costs.

## Contribution

It presents new greedy-like strategies for model adaptivity, extending existing spatial and temporal adaptivity methods, and demonstrates their superior performance in simulations.

## Key findings

- Novel strategies outperform current methods in computational efficiency
- The combined adaptivity approach effectively reduces simulation error
- Strategies are validated through realistic gas flow simulations

## Abstract

A model hierarchy that is based on the one-dimensional isothermal Euler equations of fluid dynamics is used for the simulation and optimisation of gas flow through a pipeline network. Adaptive refinement strategies have the aim of bringing the simulation error below a prescribed tolerance while keeping the computational costs low. While spatial and temporal stepsize adaptivity is well studied in the literature, model adaptivity is a new field of research. The problem of finding an optimal refinement strategy that combines these three types of adaptivity is a generalisation of the unbounded knapsack problem. A refinement strategy that is currently used in gas flow simulation software is compared to two novel greedy-like strategies. Both a theoretical experiment and a realistic gas flow simulation show that the novel strategies significantly outperform the current refinement strategy with respect to the computational cost incurred.