A time-adaptive algorithm for pressure dominated flows: a heuristic estimator

TL;DR

This paper introduces a heuristic, time-adaptive algorithm for pressure-dominated CFD and FSI problems, utilizing a novel error estimator based on BDF methods to better capture transient pressure dynamics.

Contribution

It presents a new timestep-adaptive algorithm that uses a single nonlinear solver correction for BDF2 and BDF3 to improve pressure-dominated flow simulations.

Findings

Effective in capturing fast pressure transients

Validated on backward-facing step flow CFD case

Successful application to haemodynamics FSI benchmark

Abstract

This work aims to introduce a heuristic timestep-adaptive algorithm for Computational Fluid Dynamics (CFD) and Fluid-Structure Interaction (FSI) problems where the flow is dominated by the pressure. In such scenarios, many time-adaptive algorithms based on the interplay of implicit and explicit time schemes fail to capture the fast transient dynamics of pressure fields. We present an algorithm that relies on a temporal error estimator using Backward Differentiation Formulae (BDF$k$) of order $k=2,3$. Specifically, we demonstrate that the implicit BDF$3$ solution can be well approximated by applying a single Newton-type nonlinear solver correction to the implicit BDF$2$ solution. The difference between these solutions determines our adaptive temporal error estimator. The effectiveness of our approach is confirmed by numerical experiments conducted on a backward-facing step flow CFD test case with Reynolds number $300$ and on a two-dimensional haemodynamics FSI benchmark.