# Doubly-Adaptive Artificial Compression Methods for Incompressible Flow

## TL;DR

This paper introduces adaptive artificial compression algorithms for incompressible flow that independently adjust time-step and compression parameters, supported by analysis and numerical validation, with minimal added complexity.

## Contribution

It presents novel adaptive algorithms that independently tune time-step and artificial compression parameters, supported by theoretical analysis and numerical experiments.

## Key findings

- Adaptive methods effectively control errors in incompressible flow simulations.
- The algorithms maintain low computational complexity comparable to simpler methods.
- Both first and second-order schemes are successfully embedded and tested.

## Abstract

This report presents adaptive artificial compression methods in which the time-step and artificial compression parameter $\varepsilon $ are independently adapted. The resulting algorithms are supported by analysis and numerical tests. The first and second-order methods are embedded. As a result, the computational, cognitive and space complexities of the adaptive $% \varepsilon ,k$ algorithms are negligibly greater than that of the simplest, first-order, constant $\varepsilon ,$ constant $k$ artificial compression method.