A Time-Adaptive Algorithm for Pressure Dominated Flows: A Heuristic Estimator

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 (BDFk) of order k=2,3. Specifically, we demonstrate that the implicit BDF3 solution can be well approximated by applying a single Newton-type nonlinear solver correction to the implicit BDF2 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.